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	<title>centresource interactive agency blog</title>
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	<link>http://blog.centresource.com</link>
	<description>web development &#124; nashville, tn</description>
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	<itunes:summary>web development | nashville, tn</itunes:summary>
	<itunes:author>CentreSource</itunes:author>
	<itunes:explicit>no</itunes:explicit>
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		<itunes:name>CentreSource</itunes:name>
		<itunes:email>podcast@centresource.com</itunes:email>
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	<managingEditor>podcast@centresource.com (CentreSource)</managingEditor>
	<itunes:subtitle>web development | nashville, tn</itunes:subtitle>
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		<title>centresource interactive agency blog</title>
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		<link>http://blog.centresource.com</link>
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		<item>
		<title>It&#039;s A Trap (For Us All)</title>
		<link>http://blog.centresource.com/2012/05/14/a-trap-for-us-all/</link>
		<comments>http://blog.centresource.com/2012/05/14/a-trap-for-us-all/#comments</comments>
		<pubDate>Mon, 14 May 2012 19:27:18 +0000</pubDate>
		<dc:creator>Evan Owens</dc:creator>
				<category><![CDATA[Company News]]></category>
		<category><![CDATA[Miscellaneous]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4246</guid>
		<description><![CDATA[This morning in our team meeting, I spoke about a common struggle we  face as people interpersonally. It affects our...]]></description>
			<content:encoded><![CDATA[<p>This morning in our<a  href="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/05/ackbar.gif" class="thickbox no_icon" rel="gallery-4246" title="It's a Trap"><img class="alignright size-full wp-image-4253" title="It's a Trap" src="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/05/ackbar.gif" alt="" width="288" height="374" /></a> team meeting, I spoke about a common struggle we  face as people interpersonally. It affects our personal and professional  lives equally and can have repercussions further than we can imagine.  It's the topic of "offenses." The topic of conflict resolution is never  out-of-date because it is a timeless struggle for business leaders.</p>
<p>We've all been there...where we either offended someone or were  offended. Recently in a team meeting, I made a passive aggressive comment  as a joke that was received as disrespectful and hurtful. When a team  member corrected me on the offense, I did exactly what many of us are  tempted to do and began to try and build consensus among other employees  that I wasn't out of line. However, that plan backfired when they all  agreed that I was out of line. So my plan to build an army of people who  saw my viewpoint didn't exist.</p>
<p>Anytime I've offended or been offended, a trap is set. I have two choices:</p>
<p>1 - to step into the trap and go deeper down a path of anger, resentment and bitterness</p>
<p>2 - to recognize the trap and avoid it all together, but rather proceed down a path of forgiveness and reconciliation</p>
<p>In the case above, I made the wrong decision and instead of accepting  the advice and asking for reconciliation, I proceeded down a path of  deeper frustration and gossip. This is affecting our culture and  businesses across the country. In a culture of easily offended people,  we often find ourselves on one of the two sides of the same "offense"  coin.</p>
<p>At CentreSource, we envision a culture of openness, transparency and  honesty. On one hand, we strive to give each other the benefit of the doubt  and avoid being "over-sensitive." However, on the other hand, we seek to  quickly resolve offenses when they've happened. Because when you step  into a trap what begins to happen is that all the characteristics of the  offense begin to show up in other relationships. We almost begin  looking for the signs of the offense in situations where there isn't an  offense at all.</p>
<p>By this, we limit ourselves from progress and because of an offense  we are still carrying around, we miss opportunities for personal and  professional growth. So I've been working diligently to quickly resolve  my conflicts with others and to let those from the past off the hook.  Because in many cases, I've found it amazing that my resentment and  bitterness isn't even hurting the person who offended me...it's only  hurting me. They aren't even probably aware of the offense. That, by  definition, is a trap.</p>
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		<title>The Excellent Employee</title>
		<link>http://blog.centresource.com/2012/05/02/the-excellent-employee/</link>
		<comments>http://blog.centresource.com/2012/05/02/the-excellent-employee/#comments</comments>
		<pubDate>Wed, 02 May 2012 19:13:24 +0000</pubDate>
		<dc:creator>Evan Owens</dc:creator>
				<category><![CDATA[Miscellaneous]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4242</guid>
		<description><![CDATA[I'm very fortunate here at Centresource to manage a team of excellent employees. Recently one of them sent me an...]]></description>
			<content:encoded><![CDATA[<p>I'm very fortunate here at Centresource to manage a team of excellent employees. Recently one of them sent me <a  href="http://www.inc.com/jeff-haden/the-8-qualities-of-remarkable-employees.html">an article published by Inc. Magazine</a> that listed the top eight characteristics of a remarkable employee. I'm thrilled to say our team could be the poster children for this model. The top items on their list where:</p>
<ul>
<li><strong>Ignore job descriptions</strong> - They adapt quickly to shifting priorities by doing what it takes, regardless of their job role.</li>
<li><strong>Eccentric</strong> - They stand out and are comfortable enough in their own skin to be confident</li>
<li><strong>Know when to dial it back</strong> - They know when something is serious and when it's funny</li>
<li><strong>Publicly praise</strong> - They recognize the contributions of others in public forums</li>
<li><strong>Privately complain</strong> - They come to you before and after a meeting to discuss sensitive topics rather than lead the group astray</li>
<li><strong>Speak when others won't</strong> - They have an innate feel for the issues and concerns of those around them</li>
<li><strong>Prove others wrong</strong> - They are driven by something deeper and more personal than just a desire to do a good job</li>
<li><strong>Always fiddling</strong> - They make existing progresses better all the time.</li>
</ul>
<p>If you scored your team individually on each one of these attributes (1-5) how would they score? If there are areas that are low, focus on those within your organization and tell your leaders that they have to model these attributes. As they model, others will emulate.</p>
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		<title>Share a Minnie Moment</title>
		<link>http://blog.centresource.com/2012/04/09/share-a-minnie-moment/</link>
		<comments>http://blog.centresource.com/2012/04/09/share-a-minnie-moment/#comments</comments>
		<pubDate>Mon, 09 Apr 2012 14:12:11 +0000</pubDate>
		<dc:creator>Matthew Phillips</dc:creator>
				<category><![CDATA[Interactive Strategy]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4237</guid>
		<description><![CDATA[About 25 years ago the Minnie Pearl Cancer Foundation was formed helping adults affected by cancer gain easier access to...]]></description>
			<content:encoded><![CDATA[<p>About 25 years ago the Minnie Pearl Cancer Foundation was formed helping adults affected by cancer gain easier access to resources for support, information and research in their communities. Now, 25 years later in celebration of Minnie Pearl and the spirit of her generosity, The Minnie Pearl Cancer Foundation wants to hear from you. Those they have served: caregivers, survivors, and Minnie fans. Thus, the Minnie Moments campaign was formed. The Minnie Moments campaign honors the fact that this year overlaps the 25th anniversary of the organization with the 100th birthday of the comedienne. What great timing!</p>
<p>For those of you unfamiliar, the Minnie Pearl team focuses on removing barriers for people living with cancer diagnosis, provides one-on-one guidance and counseling. We are proud to work along side such philanthropic professionals.  Make sure to check out the Minnie Moments <a  href="https://www.minniepearl.org/minniemoments?utm_source=centresource&#038;utm_medium=blog&#038;utm_campaign=minniemoments">site</a> to read the stories of those impacted and share your story.  Or keep up with everything on Minnie's <a  href="https://www.facebook.com/pages/The-Minnie-Pearl-Cancer-Foundation/81806813365">Facebook</a> and <a  href="https://twitter.com/#%21/MinniePearlHope">Twitter</a> accounts.</p>
<p>Also don't forget to join the Minnie Pearl Cancer Foundation at the upcoming <a  href="https://www.minniepearl.org/events/upcoming_events/hats_across_the_row">Hats Across the Row</a> on April 17th at 3pm on Music Row. The event is a campaign honoring Minnie's legacy and the connection between Music Row and The Minnie Pearl Cancer Foundation. It is just another celebration of the organization's 25 years of service.</p>
]]></content:encoded>
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		<title>Who Speaks Digital Archive</title>
		<link>http://blog.centresource.com/2012/03/09/who-speaks-digital-archive/</link>
		<comments>http://blog.centresource.com/2012/03/09/who-speaks-digital-archive/#comments</comments>
		<pubDate>Fri, 09 Mar 2012 16:00:14 +0000</pubDate>
		<dc:creator>Jon Arnold</dc:creator>
				<category><![CDATA[Miscellaneous]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4214</guid>
		<description><![CDATA[Who Speaks for the Negro?


This week Vanderbilt in conjunction with CentreSource launched a site dedicated to the timeless...]]></description>
			<content:encoded><![CDATA[<p><a  href="http://whospeaks.library.vanderbilt.edu/"></a></p>
<p><a href="http://whospeaks.library.vanderbilt.edu/"> </a></p>
<div class="mceTemp mceIEcenter"><a  href="http://whospeaks.library.vanderbilt.edu/"></a>
<dl id="attachment_4222" class="wp-caption aligncenter" style="width: 479px;"><a href="http://whospeaks.library.vanderbilt.edu/"></a>
<dt class="wp-caption-dt"><a  href="http://whospeaks.library.vanderbilt.edu/"></a><a href="http://whospeaks.library.vanderbilt.edu/"><img class="size-full wp-image-4222  " title="Screen Shot 2012-03-08 at 11.54.44 PM" src="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/03/Screen-Shot-2012-03-08-at-11.54.44-PM1.png" alt="Who Speaks for the Negro?" width="469" height="104" /></a></dt>
<dd class="wp-caption-dd">Who Speaks for the Negro?</dd>
</dl>
</div>
<p>This week Vanderbilt in conjunction with CentreSource launched a site dedicated to the timeless work of Robert Penn Warren. We are so excited! This was a major undertaking for both our staff and the Robert Penn Warren team at Vanderbilt.</p>
<p>In 1965, Random House published Robert Penn Warren’s book titled <em>Who Speaks for the Negro? </em>In preparation for writing the volume, Warren traveled throughout the United States in early 1964 and spoke with large numbers of men and women who were involved in the U.S. Civil Rights Movement. He interviewed nationally-known figures as well as people working in the trenches of the movement whose names might otherwise be lost to history.  In each case, he recorded their conversations on a reel-to-reel tape recorder.</p>
<p>The portal provides searchable audio interviews that will be invaluable to researchers, scholars and students. All of the contents from those interviews have been digitized and compiled and are finally available to public. Content organization was a critical goal during this initiative and this site presents a large volume of content in a highly useable format. Check out more at <a  href="http://whospeaks.library.vanderbilt.edu/">whospeaks.library.vanderbilt.edu</a>.</p>
<p>&nbsp;</p>
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		<title>Tennessean: Mobile application market heating up</title>
		<link>http://blog.centresource.com/2012/02/24/tennessean-mobile-application-market-heating-up/</link>
		<comments>http://blog.centresource.com/2012/02/24/tennessean-mobile-application-market-heating-up/#comments</comments>
		<pubDate>Fri, 24 Feb 2012 20:01:05 +0000</pubDate>
		<dc:creator>Matthew Phillips</dc:creator>
				<category><![CDATA[Company News]]></category>
		<category><![CDATA[iPhone OS]]></category>
		<category><![CDATA[Miscellaneous]]></category>
		<category><![CDATA[Mobile]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4211</guid>
		<description><![CDATA[This past Sunday, the Tennessean published an article around the recent surge in mobile application development in Nashville. One of...]]></description>
			<content:encoded><![CDATA[<p>This past Sunday, the Tennessean published an article around the recent surge in mobile application development in Nashville. One of those interviewed was one of our most recent clients, PureSweat. PureSweat offers specialized basketball training and development programs to top high school, college and NBA players. Their program enhances player's skills and fundamentals, which allow them to be successful at any level. PureSweat's owner, Drew Hanlen is currently finishing up his senior year at Belmont University. We wish Drew and the rest of the Belmont team huge success during the March Madness season.  We are very excited to have the opportunity to work on such an amazing product and driven entrepreneur.</p>
<p>You can <a  href="http://www.tennessean.com/article/20120219/BUSINESS04/302190056/-App-economy-heats-up-consumers-go-mobile" target="_blank">read the article on the Tennessean</a>.</p>
]]></content:encoded>
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		<title>A Year of ROWEing</title>
		<link>http://blog.centresource.com/2012/02/21/a-year-of-roweing/</link>
		<comments>http://blog.centresource.com/2012/02/21/a-year-of-roweing/#comments</comments>
		<pubDate>Tue, 21 Feb 2012 18:43:28 +0000</pubDate>
		<dc:creator>Shaun Jackson</dc:creator>
				<category><![CDATA[Company News]]></category>
		<category><![CDATA[Miscellaneous]]></category>
		<category><![CDATA[Operations]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4196</guid>
		<description><![CDATA[The beginning of 2012 means that it’s been a full year since the leadership team of Centresource took an enormous...]]></description>
			<content:encoded><![CDATA[<p><a  href="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/02/cubicles1.jpg" class="thickbox no_icon" rel="gallery-4196" title="cubicles"><img class="aligncenter size-full wp-image-4198" title="cubicles" src="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/02/cubicles1.jpg" alt="" width="500" height="300" /></a>The beginning of 2012 means that it’s been a full year since the leadership team of Centresource took an enormous leap of faith and did away with start and end times for the workday, and allowed employees to work from any location desired.  Around the halls of Centresource, you’ll hear it referred to as the ROWE system or “going ROWE,” referring to the Results-Only Work Environment philosophy.</p>
<p>The way that ROWE plays out at Centresource is that each employee has a certain metric that he or she is required to meet, such as a certain number of billable hours tracked each week, and as long as that goal is met, when or where it is done doesn’t matter.  In order to ensure that employees could still do their job, team members must be reachable on weekdays between 8am and 6pm, either by phone or instant message.</p>
<p>So, now, after a year of ROWE, we thought it appropriate to stop and take stock of what the staff and leadership of Centresource think, with a year of ROWE experience behind them.  We asked the team to share some of their initial fears, what unexpected benefits were realized, and in general, their thoughts on one year of ROWE.  Here’s what the team had to say:</p>
<p>Centresource President and Founder, Nicholas Holland, commented that on “...the first day of ROWE, the office was a ghost town. Actually, it was a ghost town the whole week.”  It stressed him out. “Everyone kept encouraging me to sweat through it and deal with it, and sure enough: the metrics were being met.”</p>
<p>CEO Evan Owens -- “I was nervous about the morale / unity of the team. With team members in various locations I feared that we might lose some camaraderie. However, it's improved as we now have very clear expectations of ‘what matters’ for each other rather than potentially getting frustrated by the smallest things.”</p>
<p>COO Chris Wage -- “The flexibility it gives is amazing. Getting sick is no longer an existential dilemma of whether or not I want to sacrifice a half-vacation day to sleep in. I merely sleep in, medicate myself, and then work late. The separation between your home and work life can get even foggier, so you have to be diligent in keeping it separated.  We were concerned that our ability to stay on top of metrics and performance might be difficult, but so far so good.”</p>
<p>CIO Chip Hayner -- “ROWE has removed all traces of guilt that used to exist around the office: guilt that traffic (or one too many times hitting the sleep button) caused you to be 5 minutes late, guilt that you had to run an afternoon errand (so you worked through lunch), guilt that your lunch break took 10 minutes longer than expected... Instead, these feelings have been replaced with an expectation that a) you're reachable if needed, and b) your work will get done -- something that everyone has easily stepped up to reach.”</p>
<p>Manager of strategic consulting Will Acuff -- “ROWE has been phenomenal. I love the flexibility it has allowed me and my family. I've noticed a few communication gaps but nothing that has been anywhere close to my worst case scenarios. All in all I think it has been a great success for CS.”</p>
<p>Strategic consultant Patrick Quicci -- “ROWE was one of the deciding factors for me in taking a job with CentreSource.  I love having the ability to work remotely and on my own time depending on what my schedule entails.”</p>
<p>Strategic consultant Matt Phillips -- “I have loved working under ROWE.  The biggest shift in my normal 8-5 mode has been avoiding peak traffic times.  I live 40 minutes away on a good day, but its taken up to 90 minutes to drive home on certain days.  With ROWE, I can anticipate the weather issues and come in late or leave early.  That’s time I get back in my life which was always lost.  Its been huge.”</p>
<p>Manager of interactive consulting Katy Ludington -- “ROWE has been amazing. It has meant less stress and more productivity which has been the key to my success. If I'm up late working, I don't feel like I have to rush in the office as soon as I get up in the morning.  I honestly think I work more since ROWE was introduced because I feel like the metrics we have to hit are more closely monitored and I want to keep the system going.”</p>
<p>Strategic consultant Jon Arnold -- “Having come from the corporate world, ROWE is like a breath of fresh air. I'm used to being nagged for not showing up on time.  I've enjoyed this team's approach to working together: there is no condescension for not being in the office, and working remotely is actually encouraged.  I have found working from home or remote to be so inspiring and productive (although our office and team is pretty awesome).”</p>
<p>Developer David Calhoun -- “ROWE is great. It negates a lot of stress about work. I love the ability to just take a break in the middle of the day, if things just aren't rolling or I can't focus. I can always just pick work back up later in evening.”</p>
<p>And for more inspiration on ROWE, here’s what inspired Nick Holland to make the change in the first place.  First, Nick found this thoughtful <a  href="http://positivesharing.com/2011/01/a-question-for-ya-what-do-you-do-about-employees-who-are-always-late-for-work/" target="_blank">blog post</a> on dealing with late employees.  The post impacted him, but what really changed his mind was the comments.  They took the blog post to task and really suggested a new way of dealing with employees and their time.</p>
<p>And if you have time, dig into this <a  href="https://docs.google.com/present/embed?id=d9362n5_25gf5dzxxm&#038;size=l" target="_blank">amazing presentation on Netflix’s corporate culture</a>.  Nick found it incredibly inspirational for our ROWE implementation.  It’s massive, complex, and full of amazing thoughts on how a corporation should treat it’s employees.</p>
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		<title>Are you Pinterested?</title>
		<link>http://blog.centresource.com/2012/02/20/are-you-pinterested/</link>
		<comments>http://blog.centresource.com/2012/02/20/are-you-pinterested/#comments</comments>
		<pubDate>Mon, 20 Feb 2012 21:17:17 +0000</pubDate>
		<dc:creator>Vanessa Frye</dc:creator>
				<category><![CDATA[Interactive Strategy]]></category>
		<category><![CDATA[Social Media]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4181</guid>
		<description><![CDATA[With interactive marketing being so largely concerned with engagement through web and mobile  presences, social media tends to play a...]]></description>
			<content:encoded><![CDATA[<p><a  href="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/02/Pinterest_logo.png" class="thickbox no_icon" rel="gallery-4181" title="Pinterest logo"><img class="alignleft size-medium wp-image-4193" style="border: 0pt none; margin: 5px;" title="Pinterest logo" src="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/02/Pinterest_logo-300x75.png" alt="" width="300" height="75" /></a>With interactive marketing being so largely concerned with engagement through web and mobile  presences, social media tends to play a major role in conversions.  As  of late, social media platform <a  href="http://www.pinterest.com">Pinterest</a>, has reared it's lovely head.   As an avid recipe-finding, fitness-seeking, outfit-shopping junky, this  site has proved to feed my addiction.  While the obsession has become  widespread, there are still lots of people unaware of this phenomenon.</p>
<p>Some may wonder what Pinterest actually is and why it is so  'Pinteresting'.  Sorry, I can't help myself.  Pinterest is a vision  board-styled social photo sharing site especially popular among women.   The site and iPhone app allow users to create and manage theme-based  image collections.</p>
<p>The site's mission statement is to 'connect everyone  in the world through the 'things' they find interesting.'  So how can,  yet another, social media platform help your brand, you ask?  Brands and  companies can host contests with competitors for 'best boards' while  getting their consumers' involvement.  Got a new product that hasn't  launched?  Post it to Pinterest to see what type of reaction people  have.  It's like a social media focus group.</p>
<p>Another way to use  Pinterest is for showcasing brand personality.  In this case, you may be  a business that is more focused on services rather than products.   Businesses have a way to connect audiences with its story, mission  and/or future plans.  If you haven't signed up yet, get to <a  href="http://www.pinterest.com/" target="_blank">www.pinterest.com</a> and do it!  If you need an invite, send me an email at <a  href="mailto:vanessafrye@gmail.com" target="_blank">vanessafrye@gmail.com</a> and I'll be sure to invite you.  Get out there and start pinning!</p>
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		<title>February Mixer!</title>
		<link>http://blog.centresource.com/2012/02/17/february-mixer/</link>
		<comments>http://blog.centresource.com/2012/02/17/february-mixer/#comments</comments>
		<pubDate>Fri, 17 Feb 2012 23:39:39 +0000</pubDate>
		<dc:creator>Jon Arnold</dc:creator>
				<category><![CDATA[Miscellaneous]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4184</guid>
		<description><![CDATA[&#160;

&#160;
It's that time again: the FIRST #CSMixer of 2012!  Come on out to catch up, network and generally...]]></description>
			<content:encoded><![CDATA[<p style="text-align: center;">&nbsp;</p>
<p><a  href="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/02/2814764.web_.jpeg" class="thickbox no_icon" rel="gallery-4184" title="Centresource February Mixer!"><img class="alignnone size-full wp-image-4185" title="Centresource February Mixer!" src="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/02/2814764.web_.jpeg" alt="Centresource February Mixer!" width="504" height="360" /></a></p>
<p>&nbsp;</p>
<p>It's that time again: the FIRST #CSMixer of 2012!  Come on out to catch up, network and generally geek out!  We'll have great finger foods and beer graciously provided by our friends at <a  title="Blackstone Brewery" href="http://blackstonebrewery.com/" target="_blank">Blackstone</a>.</p>
<p>So <a  title="RSVP for the February Mixer!" href="http://centresource.pingg.com/February2012">be sure you RSVP</a>, and we'll see you all on Thursday!</p>
]]></content:encoded>
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		<item>
		<title>Responsive Web</title>
		<link>http://blog.centresource.com/2012/02/01/responsive-web/</link>
		<comments>http://blog.centresource.com/2012/02/01/responsive-web/#comments</comments>
		<pubDate>Wed, 01 Feb 2012 16:02:46 +0000</pubDate>
		<dc:creator>Vanessa Frye</dc:creator>
				<category><![CDATA[Mobile]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=4174</guid>
		<description><![CDATA[Recently I wrote a blog and an article about the difference between mobile apps and mobile sites.  (Be sure to...]]></description>
			<content:encoded><![CDATA[<p>Recently I wrote <a  href="http://blog.centresource.com/2011/10/31/mobile-app-mobile-site/">a blog </a>and an article about the difference between mobile apps and mobile sites.  (Be sure to check out my article in the  <a  href="http://issuu.com/nashvilletechnologycouncil/docs/catalyst_2012">NTC's Catalyst Magazine from January 25th</a>).  I knew as soon as I  wrote about the topic, a new technology would come swooping down and  steal the show.  That technology, my friends, is the Responsive Web.  If you  haven't heard of it, you better start learning - it will pretty much  blow your mind.</p>
<p>So what's all the fuss about?  Each month, statistics pour in that reveal a heavy increase of mobile users over traditional desktop web platforms.  In response to this, designers and developers have begun to focus on building websites and applications that work appropriately on all sorts of screens, regardless on the device type.  The official definition:  Responsive Web design is a way of  organizing page layout and information to ensure that a web page responds to  the device in which it's viewed.  While the same content is being displayed regardless of the device, the content is set to display differently depending on the device's screen size.</p>
<p>Have you ever gone to a website from Safari on your  phone (I'm an Apple fan girl, obviously) and were disappointed at all  the pinching and squeezing required just to get a phone number?  Or an  address?  Responsive Web will alleviate that pain by displaying the same  content you would see on your laptop, just in a better and easier to  read format.  Still not convinced?  Check out some of these examples:  <a  href="http://www.knowshelter.com/" target="_blank">www.knowshelter.com</a>, <a  href="http://www.morehazards.com/" target="_blank">www.morehazards.com</a> and <a  href="http://www.forefathersgroup.com/" target="_blank">www.forefathersgroup.com</a></p>
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		<title>Freakin&#039; asymptotic notation: How does that work?</title>
		<link>http://blog.centresource.com/2012/01/23/freakin-asymptotic-notation-how-does-that-work/</link>
		<comments>http://blog.centresource.com/2012/01/23/freakin-asymptotic-notation-how-does-that-work/#comments</comments>
		<pubDate>Mon, 23 Jan 2012 18:15:32 +0000</pubDate>
		<dc:creator>Jeremy Holland</dc:creator>
				<category><![CDATA[Miscellaneous]]></category>
		<category><![CDATA[Theory]]></category>
		<category><![CDATA[Web Development]]></category>

		<guid isPermaLink="false">http://blog.centresource.com/?p=3623</guid>
		<description><![CDATA[OK, I'll be the first to admit it - math is my favorite subject. I know that makes me weird...]]></description>
			<content:encoded><![CDATA[<p>OK, I'll be the first to admit it - math is my favorite subject. I know that makes me weird - even among fellow working software engineers - but it's the truth. It's also the truth that while they may be boring to many, knowing even a little bit about the numbers of computer science can help make you a better software engineer. Today, we're going to look at a little piece of applied discrete math - the analysis of algorithms - and how we can empirically describe the performance of one algorithm with respect to another using something called "asymptotic notation". If you already know what this is and how to read the various sub-notations, skip the rest of this post: it's old news. If you do not know what this is, and would like to, read on! If you do not know what this is and don't care, read on anyway - I promise you it'll be worth it.</p>
<p>Now, while I'm totally guilty of bandying around big scary terms like "asymptotic notation" (I'm a notorious stickler for nomenclature), what this boils down to is the following mathematical notation (and its related brothers, which we'll get to later):</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_86170f0037842246df67f90ab032cf23.gif' style='' class='tex' alt="O(g(n)) " /></span></p></p>
<p>Most typically, you'll see this used and referred to not as <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_86170f0037842246df67f90ab032cf23.gif' style=' ' class='tex' alt="O(g(n)) " /></span>, which doesn't serve much purpose unless we know already what <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_9a4aa4746e3b82145ff1af2052b1325f.gif' style=' ' class='tex' alt="g(n) " /></span> is, but rather in terms of a <strong>specific</strong> <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_9a4aa4746e3b82145ff1af2052b1325f.gif' style=' ' class='tex' alt="g(n) " /></span>, say, <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3ac3bd4c4c1f66111feb1ef16babaad6.gif' style=' padding-bottom:1px;' class='tex' alt="n^2 " /></span>:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_14fd02f6323f8a36e2bb5abc3af32923.gif' style='' class='tex' alt="O(n^2) " /></span></p></p>
<p>Moreover, for the purposes of this discussion, we're going to look primarily at the following notation style:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_f7dd4a60bc10c04a4c3da54cb9742773.gif' style='' class='tex' alt="f(n) = O(n^2) " /></span></p></p>
<p>So what on earth does this mean? Well, let's think about algorithms. What is an algorithm? Simply a series of instructions for performing some task, right? In computing specifically an algorithm is implemented as an actual, written program in your language of choice. But under the hood, mathematically, an algorithm is a <strong>function</strong> (sometimes pure, sometimes not): it takes some input(s) and delivers some output. In the above block o' math, let us equate <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_996cb805d9bfdfe8d06fed3a6f842841.gif' style=' ' class='tex' alt="f(n) " /></span> with some algorithm we would like to implement, say, sorting an array of integers from least to greatest. With an algorithm such as that, you would give it an array of dubiously sorted values, and it would give you back an array containing exactly the same elements but in sorted order. Represented mathematically, we have:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_a37aa991945fb7f4c4d9ce2a2485a695.gif' style='' class='tex' alt="s(a) " /></span></p></p>
<p>where <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_ff705f1b6f527fe2038d5ad152f64769.gif' style=' padding-bottom:2px;' class='tex' alt="s " /></span> is the algorithm function itself, and <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_99020cb24bd13238d907c65cc2b57c03.gif' style=' padding-bottom:2px;' class='tex' alt="a " /></span> is the array to be sorted. Now, let's keep in mind that there are many different ways of going about sorting an array - naturally, we would like to pick the fastest one for the task at hand. So in order to know anything about the <em>performance</em> of an algorithm, we should probably come up with some way to represent how long it takes to run. To wit:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_c9e5188fdbbb8ce19aecbcebe72f2bd9.gif' style='' class='tex' alt="T(s(a)) " /></span></p></p>
<p>represents the "time" <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3b85a149146b36ea27855e7e05656385.gif' style=' padding-bottom:1px;' class='tex' alt="T " /></span> it takes to run algorithm <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_ff705f1b6f527fe2038d5ad152f64769.gif' style=' padding-bottom:2px;' class='tex' alt="s " /></span> on input <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_99020cb24bd13238d907c65cc2b57c03.gif' style=' padding-bottom:2px;' class='tex' alt="a " /></span>. OK. So, how can we begin to reason about what the range of this function might be? Actually, perhaps that's jumping the gun - what would really be the <em>domain</em> of this function? What measurement of your general work-a-day sorting algorithm would dictate how long it takes to run? The answer, my friend, is the size of the input: it should make sense to anybody who's actually had to do it that sorting a 10-element array is a heck of a lot faster than sorting a 10,000,000-element array. So, really, our <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3b85a149146b36ea27855e7e05656385.gif' style=' padding-bottom:1px;' class='tex' alt="T " /></span> function can be abstracted further as a function of <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6fa45c22bd311a4aa532cffb668d86a0.gif' style=' padding-bottom:2px;' class='tex' alt="n " /></span>, where <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6fa45c22bd311a4aa532cffb668d86a0.gif' style=' padding-bottom:2px;' class='tex' alt="n " /></span> is the size of the array to be sorted:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_4df613dbccbdf85fc2a66aca70969a9c.gif' style='' class='tex' alt="T(n) " /></span></p></p>
<p>Since the value of <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_4df613dbccbdf85fc2a66aca70969a9c.gif' style=' ' class='tex' alt="T(n) " /></span> will grow as <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6fa45c22bd311a4aa532cffb668d86a0.gif' style=' padding-bottom:2px;' class='tex' alt="n " /></span> grows (presumably), this seems like a solid footing to start our thinking upon.</p>
<p>Alrighty. Now that we've got some notation to start thinking about how we'll build this bad boy, let's actually pick a real, concrete algorithm and think through it. For the purposes of simplicity and succinctness (cue laughter), I'm going to go with <a  href="http://en.wikipedia.org/wiki/Bubble_sort">Bubble Sort</a>. If you want to learn more about the actual algorithm, I suggest you read the wikipedia article linked to above, because I'm gonna skip over a fat exposition on what it actually does and how it does it in favor of thinking about how long it <em>takes</em> to do it, and specifically how long it takes to do it to the worse possible case of input: an array that's already been sorted, but reversed. Please note I have copied the following pseudocode directly from wikipedia, and credit therefor is due directly to the author of the page linked to above.</p>
<div style="float: right; text-align: right; line-height: 20px;"><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_f5a8dc2100232317501798aef2136fce.gif' style=' padding-bottom:2px;' class='tex' alt="c_{1} " /></span><br />
<span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_46a0953f49dc908f517f7b8e3599ce0f.gif' style=' padding-bottom:2px;' class='tex' alt="c_{2} " /></span><br />
<span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_34e67db8f2efedeb7c00cc787613a2b2.gif' style=' padding-bottom:2px;' class='tex' alt="c_{3}n " /></span><br />
<span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_56bc9141c4b140d44b8cb4ffc44b593f.gif' style=' padding-bottom:2px;' class='tex' alt="c_{4}n " /></span><br />
<span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_29fbc20da3471cfac95817e174c6508f.gif' style=' ' class='tex' alt="c_{5}n(n-1) " /></span><br />
<span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_114f1abc3d8cb8ac60905e49c99f9460.gif' style=' ' class='tex' alt="c_{6}n(n-1) " /></span><br />
<span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_bb8bbb4afe68d6c721e7ff95e3a86d88.gif' style=' ' class='tex' alt="c_{7}n(n-1) " /></span></p>
<p><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_83e966c8380f5364e394ea832dbeb3be.gif' style=' padding-bottom:2px;' class='tex' alt="c_{8}n " /></span></p></div>
<div style="line-height: 20px;">procedure bubbleSort( A : list of sortable items )<br />
repeat<br />
swapped = false<br />
for i = 1 to length(A) - 1 inclusive do:<br />
if A[i-1] &gt; A[i] then<br />
swap( A[i-1], A[i] )<br />
swapped = true<br />
end if<br />
end for<br />
until not swapped<br />
end procedure</div>
<p>OK, so that's the algorithm from wikipedia - but what's all that nasty-looking business on the right? Put quite simply, that's our best guess as to how long that line of code takes to execute! Note that each line is some function of <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6fa45c22bd311a4aa532cffb668d86a0.gif' style=' padding-bottom:2px;' class='tex' alt="n " /></span> and some constant <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_270988921d2d88e2bf292f4caccb0845.gif' style=' padding-bottom:2px;' class='tex' alt="c_{i} " /></span>. Now if we wanted to figure out <em>exactly</em> how long this algorithm takes to run, we'd need to know the value of those contants, e.g. <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_c4fa814f77f2a12b7f5dc261feae338f.gif' style=' padding-bottom:1px;' class='tex' alt="c_{1} = 12.2ms " /></span> or something. You'll notice that some lines <em>only</em> seem to take a constant time to run; that's because those lines are only executed once <em>regardless of how big the input is</em>. Other lines are the associated constant multiplied by <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6fa45c22bd311a4aa532cffb668d86a0.gif' style=' padding-bottom:2px;' class='tex' alt="n " /></span> - those lines will execute once for every unit of input. Still others are multiplied by <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3098b1083ac981b7c728533cfa4fbafe.gif' style=' ' class='tex' alt="n(n-1) " /></span> - these lines are executed <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_41c82d523ef9895c903eca0ccbda03bc.gif' style=' padding-bottom:1px;' class='tex' alt="n-1 " /></span> times for each input. Now, handily, we can figure out our overall formula by just adding all these things together:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_dbca013708a4a9a62f6fff5fae63721f.gif' style='' class='tex' alt="T(n) = c_{1} + c_{2} + c_{3}n + c_{4}n + c_{5}n(n-1) + c_{6}n(n-1) + c_{7}n(n-1) + c_{8}n " /></span></p><br />
<p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6a84257bf25f7279d5f2a62b4aec3b37.gif' style='' class='tex' alt="T(n) = c_{1} + c_{2} + c_{3}n + c_{4}n + c_{5}n^{2}-n + c_{6}n^{2}-n + c_{7}n^{2}-n + c_{8}n " /></span></p><br />
<p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_321d1916a4318ce2b9b4d098602b0aa5.gif' style='' class='tex' alt="T(n) = (c_{5} + c_{6} + c_{7})n^{2} + (c_{3} + c_{4} + c_{8} - 3)n + (c_{1} + c_{2}) " /></span></p></p>
<p>But it turns out that the precise value of each constant is practically useless - the constants in question represent such complex matters and concrete facts of the real world as language of implementation, hardware specs, how many other processes are fighting for CPU time, etc. Remember that we only really care about the performance of the <em>algorithm</em> - not the performance of the hardware or implementation thereof, which is not affected by the algorithm itself. So we can happily simplify our job by just getting rid of all those pesky constants!</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_13db7c457bd0320380dc18ee50d7d8da.gif' style='' class='tex' alt="T(n) = n^{2} + n " /></span></p></p>
<p>Wow, much nicer! But guess what: it gets even simpler. Since, for large enough inputs, the contribution of the lower-order term <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6fa45c22bd311a4aa532cffb668d86a0.gif' style=' padding-bottom:2px;' class='tex' alt="n " /></span> makes virtually no difference to the output number, we can happily drop that too:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_bd661977b23acf8fe0e1efc93d998a6e.gif' style='' class='tex' alt="T(n) = n^{2} " /></span></p></p>
<p>And voilá! Unfortunately, we've boiled this timing function down so far and stripped so much from it that we can't really say that <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_4df613dbccbdf85fc2a66aca70969a9c.gif' style=' ' class='tex' alt="T(n) " /></span> is <em>exactly</em> <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_093456214537de9bf72aac04b00c55b7.gif' style=' padding-bottom:1px;' class='tex' alt="n^{2} " /></span>, just that (in the worst case) it follows a similar curve. More precisely, we have virtually guaranteed that, for large enough inputs, it can never be bigger than some constant <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_9400ebf223f50ff8fccb32ed13ea819e.gif' style=' padding-bottom:2px;' class='tex' alt="c " /></span> <em>times</em> <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_093456214537de9bf72aac04b00c55b7.gif' style=' padding-bottom:1px;' class='tex' alt="n^{2} " /></span>. This is the crux of asymptotic notation - specifically what is referred to as "Big-O notation". As such, when we say that:</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_133e9f1515189423e9a2e5248a7dba57.gif' style='' class='tex' alt="T(n) = O(n^{2}) " /></span></p></p>
<p>What we mean is that there are some constants <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_9400ebf223f50ff8fccb32ed13ea819e.gif' style=' padding-bottom:2px;' class='tex' alt="c " /></span> and <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_99020cb24bd13238d907c65cc2b57c03.gif' style=' padding-bottom:2px;' class='tex' alt="a " /></span>, such that for all <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6fa45c22bd311a4aa532cffb668d86a0.gif' style=' padding-bottom:2px;' class='tex' alt="n " /></span> where <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3f4a026870b81ff5de38c54fe0096ccd.gif' style=' padding-bottom:1px;' class='tex' alt="0 \le a < n " /></span>, we know that <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_0c92d598ba6c40ec0c8c9ab004de2b93.gif' style=' ' class='tex' alt="T(n) \le cn^{2} " /></span>.</p>
<p>It should also be pointed out that the notation's use of the "equals sign" is a little unusual - we're not saying that <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_4df613dbccbdf85fc2a66aca70969a9c.gif' style=' ' class='tex' alt="T(n) " /></span> <em>is equal to</em> <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3306139fad2e84214191fb8212060c4c.gif' style=' ' class='tex' alt="O(n^{2}) " /></span>, but that it is of equal or lesser <em>order</em> to <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_093456214537de9bf72aac04b00c55b7.gif' style=' padding-bottom:1px;' class='tex' alt="n^{2} " /></span>. This might be a bit of a trick to wrap your head around at first (it certainly was to me). If I'd have written the notation myself, I'd have tried to use some symbol that didn't already carry all the connotations and denotations the "equals sign" itself does; but c'est la vie - this is the way it's done. Another way (in fact, the proper way) to think of it is to think of <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3306139fad2e84214191fb8212060c4c.gif' style=' ' class='tex' alt="O(n^{2}) " /></span> being some set of functions that follow the above definition, and for the notation</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_133e9f1515189423e9a2e5248a7dba57.gif' style='' class='tex' alt="T(n) = O(n^{2}) " /></span></p></p>
<p>to in fact mean</p>
<p><p style='text-align:center;'><span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_00f8df56f1fe095f524dbdc010c4ea05.gif' style='' class='tex' alt="T(n) \in O(n^{2}) " /></span></p></p>
<p>i.e. that <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_4df613dbccbdf85fc2a66aca70969a9c.gif' style=' ' class='tex' alt="T(n) " /></span> is an <em>element</em> of the set <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3306139fad2e84214191fb8212060c4c.gif' style=' ' class='tex' alt="O(n^{2}) " /></span>.</p>
<p>OK, so we've been able to put an upper bound on some hypothetical order of our function <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_4df613dbccbdf85fc2a66aca70969a9c.gif' style=' ' class='tex' alt="T(n) " /></span>, but what does that really tell us? Not a whole lot, in isolation. But it really comes into play when you consider other algorithms, such as, say <a  href="http://en.wikipedia.org/wiki/Merge_Sort">Merge Sort</a>, which is bounded on top not by <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_3306139fad2e84214191fb8212060c4c.gif' style=' ' class='tex' alt="O(n^{2}) " /></span>, but by <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_6683d14c695737b36b0b60968b56c04e.gif' style=' ' class='tex' alt="O(n\log_{2}n) " /></span>! Graph those two functions and here's what you get (<span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_093456214537de9bf72aac04b00c55b7.gif' style=' padding-bottom:1px;' class='tex' alt="n^{2} " /></span> is in black, <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_d5c3a3002b4a1a4c546caea68a7a6bcd.gif' style=' ' class='tex' alt="n\log_{2}n " /></span> is in red):</p>
<p><a  href="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/01/graph-e1327292605398.png" class="thickbox no_icon" rel="gallery-3623" title="graph"><img class="alignnone size-medium wp-image-4131" title="graph" src="http://blog.centresource.com/wordpress/../wp-content/uploads/2012/01/graph-e1327292808431-300x173.png" alt="" width="300" height="173" /></a></p>
<p>This is a bit of an oversimplification, but sufficient to demonstrate the idea - notice that very quickly, <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_093456214537de9bf72aac04b00c55b7.gif' style=' padding-bottom:1px;' class='tex' alt="n^{2} " /></span> begins to overtake <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_d5c3a3002b4a1a4c546caea68a7a6bcd.gif' style=' ' class='tex' alt="n\log_{2}n " /></span>, and continues to do so, the gap getting ever wider as n gets ever bigger; and just like in golf, the lower score is the one you want.</p>
<p>So, in what I hope was nutshell-ish if not perfectly so, that's the basics of asymptotic notation! There are other, related notations like "Big Theta" <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_70cf58380aa0dadd0aefb858fa5f925f.gif' style=' ' class='tex' alt="\Theta(g(n)) " /></span>, "Big Omega" <span class='MathJax_Preview'><img src='http://blog.centresource.com/wordpress/wp-content/plugins/latex/cache/tex_aa0884f77bfcfdcaf1f0c8477a1d2dc2.gif' style=' ' class='tex' alt="\Omega(g(n)) " /></span>, and the lower-case versions of omega and o, but I'll leave those to you to explore.</p>
<p>Finally, as a disclaimer, I have tried to make the math herein as simple as possible for the purposes of the demonstration, and I could easily have borked something up terribly (I'm still getting the hang of LaTeX). If you spot an error, comment and I'll see that it's corrected. Thanks!</p>
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