Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time · HackerPapers discussions

Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time — mentioned by FooBarBizBazz

Sat, 02 Nov 2024 13:34:42 GMT

Man, there was a lot of obtuse argument to wade through to get to this post. This is an interesting fact. Apparently this is the source? https://arxiv.org/abs/cs/0111050

Paper and discussion history. A mention is not an endorsement.

Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time — mentioned by npalli

Sat, 18 Jun 2022 18:36:18 GMT

The article discusses how the two mathematicians (Spielman and Teng) came up with Smoothed Analysis for Algorithms (as opposed to Worst case) which gives insight into why Simplex works well. We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simplex…

Paper and discussion history. A mention is not an endorsement.

Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time — mentioned by luu

Mon, 06 Jun 2016 06:37:19 GMT

> If you have tens of thousands of variables, you definitely don't want to risk dealing with the simplex method's worst-case behavior. The risk is extremely low. In fact, the risk is so low that, for deacdes, it was an open question why the simplex algorithm was so good in practice on a wide variety of workloads despite having poor worst-case complexity (unlike, for example, pure quicksort, which is often problematic in practice). Spielman solved that problem in 2001 and showed that even very small perturbations from a contrived worst-case input have good performance…

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Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time — HN submission

Sun, 20 Mar 2016 12:51:41 GMT

Why the Simplex Algorithm Usually Takes Polynomial Time (2001)

3 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time — HN submission

Sun, 03 Nov 2013 23:10:07 GMT

Smoothed Analysis: Why the Simplex Algorithm Usually Takes Polynomial Time

55 points; 8 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time — mentioned by mzl

Thu, 20 Jan 2011 08:21:56 GMT

OTOH, simplex is very efficient already. Average-case complexity for random matrices is polynomial, and there are some interesting results that extend beyond that (see http://arxiv.org/abs/cs/0111050).

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Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time — HN submission

Thu, 07 Feb 2008 02:58:14 GMT

Smoothed Analysis: Why The Simplex Algorithm Usually Takes Polynomial Time.

2 points; 1 discussion reply on HN. Paper and source history. A submission is not an endorsement.