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To illustrate the potential improvements possible even in well-established algorithms, a recent significant innovation, relating to [[Fast Fourier transform|FFT]] algorithms (used heavily in the field of image processing), can decrease processing time up to 1,000 times for applications like medical imaging.<ref>{{cite web| title=Better Math Makes Faster Data Networks| author=Gillian Conahan| date=January 2013| url=http://discovermagazine.com/2013/jan-feb/34-better-math-makes-faster-data-networks| publisher=discovermagazine.com| access-date=May 13, 2014| archive-url=https://web.archive.org/web/20140513212427/http://discovermagazine.com/2013/jan-feb/34-better-math-makes-faster-data-networks| archive-date=May 13, 2014| url-status=live}}</ref> In general, speed improvements depend on special properties of the problem, which are very common in practical applications.<ref name="Hassanieh12">Haitham Hassanieh, [[Piotr Indyk]], Dina Katabi, and Eric Price, "[http://siam.omnibooksonline.com/2012SODA/data/papers/500.pdf ACM-SIAM Symposium On Discrete Algorithms (SODA)] {{webarchive|url=https://web.archive.org/web/20130704180806/http://siam.omnibooksonline.com/2012SODA/data/papers/500.pdf |date=July 4, 2013 }}, Kyoto, January 2012. See also the [http://groups.csail.mit.edu/netmit/sFFT/ sFFT Web Page] {{Webarchive|url=https://web.archive.org/web/20120221145740/http://groups.csail.mit.edu/netmit/sFFT/ |date=February 21, 2012 }}.</ref> Speedups of this magnitude enable computing devices that make extensive use of image processing (like digital cameras and medical equipment) to consume less power.
{{Main|Best, worst and average case}}
The best case of an algorithm refers to the scenario or input for which the algorithm or data structure takes the least time and resources to complete its tasks.<ref>{{Cite web |title=Best Case |url=https://xlinux.nist.gov/dads/HTML/bestcase.html |access-date=29 May 2025 |website=Dictionary of Algorithms and Data Structures |publisher=National Institute of Standards and Technology (NIST) |agency=National Institute of Standards and Technology}}</ref> The worst case of an algorithm is the case that causes the algorithm or data structure to consume the maximum period of time and computational resources.<ref>{{Cite web |title=worst case |url=https://xlinux.nist.gov/dads/HTML/worstcase.html |access-date=29 May 2025 |website=Dictionary of Algorithms and Data Structures |publisher=National Institute of Standards and Technology (NIST) |agency=National Institute of Standards and Technology (NIST)}}</ref>
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