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the P vs NP problem attracts a lot of attention, not all of it desirable, for a wide variety of reasons. there are many P=NP claims eg on this widely cited list maintained by mathematician Woegeorgi, P vs NP page. also, intermittently there are hot questions on SE sites related to P vs NP (eg recently [2],[3]) below, & there is even a p-vs-np tag on both cs.se () & tcs.se sites. the following is intended somewhat as a reference question.

what are the basic/typical/common mistakes in P=NP claims?

[1] How not to solve P=NP?, cs.se
[2] P vs NP code exercise, codegolf.se
[3] Analogs of P vs NP in the history of mathematics MO.se

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vzn
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1 Answers1

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Often, people claim to find a polytime algorithm for an NP-hard problem. A couple things could go wrong:

  1. The algorithm does not return a correct answer.
  2. The algorithm does not run in polytime.

An example of the first mistake is Ted Swart's LP formulations for TSP. They were of poly-size (and so could be solved in polytime with any polytime LP algorithm), but the formulations were not tight. (More info here.)

I have blogged about a particular case of the second mistake. The short story is that the proof of poly runtime "solved" a recurrence relation incorrectly.

Austin Buchanan
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