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The answer depends what exactly we mean by "polynomial-time" algorithms. Rigorously, an algorithm is '''polynomial-time''' if its worst-case runni However, much faster and simpler randomized primality testing algorithms were known long before the discovery of efficient deterministic primality t ...

...he dimensionality reduced data. In many cases, this approach will speed up algorithms for solving <math>k</math>-means clustering. ...

...lexity model, the local computational costs are ignored. The complexity of algorithms (also called communication protocols here) are measured by the number of bi ...

...raphs] have found extensive applications in computer science, in designing algorithms, [http://en.wikipedia.org/wiki/Error_correcting_code error correcting codes ...te. Studies of these two problems revolutionized the area of approximation algorithms. ...

For the efficiency of randomized algorithms, we are interested in the random walks that converges "fast". Measured by t * For Metropolis algorithms which generate uniform stationary distribution, <math>P_{uv}</math> are equ ...

...theory]] – [[Mathematical physics]] – [[Fluid dynamics]] - [[computational algorithms]] ...

...he dimensionality reduced data. In many cases, this approach will speed up algorithms for solving <math>k</math>-means clustering. ...

...he dimensionality reduced data. In many cases, this approach will speed up algorithms for solving <math>k</math>-means clustering. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. The [http://delivery.acm.org/10.1145/2750000/2746588/p665-kawarabayashi.pd ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. The [http://delivery.acm.org/10.1145/2750000/2746588/p665-kawarabayashi.pd ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. A deterministic algorithm of [https://dl.acm.org/citation.cfm?id=2746588 K ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. A deterministic algorithm of [https://dl.acm.org/citation.cfm?id=2746588 K ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. A deterministic algorithm of [https://dl.acm.org/citation.cfm?id=2746588 K ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. A deterministic algorithm of [https://dl.acm.org/citation.cfm?id=2746588 K ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. A deterministic algorithm of [https://dl.acm.org/citation.cfm?id=2746588 K ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...(meaning there is no parallel edges) with no edge weight, there are better algorithms. A deterministic algorithm of [https://dl.acm.org/citation.cfm?id=2746588 K ...possible instances''. This notion is formally captured by '''approximation algorithms''' and '''approximation ratio'''. ...

...tive''''' proofs that we are going to introduce later, which are basically algorithms. ...gorithm as well as its output is ''deterministic''. But for ''randomized'' algorithms, the behavior of <math>\mathsf{Alg}(r, \phi)</math> is a random variable ev ...

...raphs] have found extensive applications in computer science, in designing algorithms, [http://en.wikipedia.org/wiki/Error_correcting_code error correcting codes ...te. Studies of these two problems revolutionized the area of approximation algorithms. ...

...raphs] have found extensive applications in computer science, in designing algorithms, [http://en.wikipedia.org/wiki/Error_correcting_code error correcting codes ...te. Studies of these two problems revolutionized the area of approximation algorithms. ...