Talk:List of NP-complete problems

message: What about protein folding?  —Preceding unsigned comment added by 129.11.60.53 (talk) 16:11, 8 March 2008 (UTC)
replies: text: What about it? If you want a proof that it's hard to do: http://www.cs.berkeley.edu/~christos/hp.ps 134.58.42.46 (talk) 12:37, 1 December 2010 (UTC)
thread_title: Protein Folding

message: The Betweenness problem, as defined in the article has a polynomial algorithm and therefore is in P.
If it were an NP-Complete problem than P=NP.
I think that there is a problem with the definitions, and the one that added the betweenness problem meant to other definition.
Until the correct definition is found, I'll remove the problem from the list. APH 07:26, 30 May 2005 (UTC)
replies: text: It does belong and should be added back; see SJ. Opatrny, Total ordering problem, SIAM J. Comput., 8 (1979), pp. 111–114. Problem is MS1 in Garey, M. R.; Johnson, D. S. (1979), Computers and Intractibility: a guide to the theory of NP-completeness, W.H. Freeman, according to http://acawiki.org/Total_ordering_problem Jodi.a.schneider (talk) 09:25, 5 October 2010 (UTC)
replies: text: I no longer see betweenness on the list so I guess it was removed at some point, but it does belong (with the link JAS gave), and now has its own article; I will add it back. —David Eppstein (talk) 02:10, 20 August 2015 (UTC)
thread_title: Betweenness problem

message: Google only finds the phrase "Covering by vertex cover" on this page, so I don't think that it is distinct from Vertex Cover.  I removed it as a duplicate. James Aguilar 17:11, 29 November 2005 (UTC)
thread_title: Vertex Covering

message: Someone needs to go through and remove all of the PSPACE-complete, EXPTIME-complete, etc. problems; I have created List of PSPACE-complete problems to store the former. It might be desirable to also have List of EXPTIME-complete problems. So far I have only done the Games and Logic sections; I don't know that much about the rest (and probably made mistakes even in those sections). Ben Standeven 08:29, 30 January 2007 (UTC)
thread_title:  On harder-than-NP problems 

message: The page claims that  "intersection of finite state automata" is NP-complete. I assume that this refers to the question whether or not such an intersection is empty. But this claim appears to be unfounded. For a fixed number of automata (such as 2), the problem is clearly in PTIME: just construct the intersection automaton. For polynomial number of automata, one can find an algorithm running in PSPACE: "guess" an accepted word letter by letter, show acceptance, and use Savitch's theorem to reduce NPSpace to PSpace. Indeed, this problem is reported to be PSPACE-complete in various sources:
* The paper "PSPACE-completeness of Modular Supervisory Control Problems" (PS) states that the problem is PSpace complete, citing the following related sources: 
** D. Kozen. Lower bounds for natural proof systems. In Proc. 18th Symp. on the Foundations of Computer Science, pages 254–266, 1977.
** M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, 1979.
** K.-J. Lange and P. Rossmanith. The emptiness problem for intersections of regular languages. In I. Havel, editor, Proc. of the 17th Conf. on Mathematical Foundations of Computer Science, number 629 in LNCS, pages 346–354. Springer-Verlag, 1992.
* List of PSPACE-complete problems lists the problem with a question mark (which should probably be removed)
* http://www.cs.mun.ca/~harold/Courses/Old/Ling6800.W06/Diary/index.html states that "Finite State Automata Intersection is PSPACE-complete (Garey and Johnson (1979), Problem AL6, p. 266)" where the cited source is "Garey, M.R., and Johnson, D.S. (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman; San Francisco, CA."
I thus removed automata intersection from the article. --Markus Krötzsch 09:33, 26 March 2007 (UTC)
replies: text: You are absolutely right. I can reassure you that DFA intersection emptiness is PSPACE-complete, proved in (Kozen, 1977). Some introductory textbooks contain the fact that the problem is NP-hard (as exercise or theorem with proof), so possibly someone simply missed the difference between hardness and completeness. Hermel (talk) 22:08, 10 October 2008 (UTC)

text: Hermel, could you please list sources that say that the intersection emptiness problem is NP-hard because I was unable to find any.  — Preceding unsigned comment added by Mikew72324 (talk • contribs) 22:35, 15 August 2011 (UTC)
thread_title:  Finite state automata intersection not in NP 

message: I'm looking at this problem for some work I'm doing and it is np-complete for more than 2 machines.  I don't know if it is in the list under another name, but if not, it could be added to the list.  Just a thought.  —Preceding unsigned comment added by 71.63.82.192 (talk) 07:16, 24 September 2007 (UTC)
thread_title:  Permuatation Flow shop problem 

message: The games section needs more explanation as to what part of the game is NP-Complete.  For example, is  the problem with Sudoku to find the possible number of solved puzzles, the possible number of solvable puzzles, or what?  The Sudoku article mentions nothing about NP-Completeness (which is another thing, these things should all be mention in their respective articles).  Asmeurer (talk  ♬ contribs) 18:26, 16 November 2008 (UTC)
replies: text: The problem with Sudoku is to test whether a particular n-by-n (rather than 9-by-9) puzzle can be completed to a solution. However, NP-completeness is a bit of an issue because the usual reductions involve problems that may have multiple solutions while Sudoku puzzles are generally required to have exactly one. There's a workaround involving Valiant and Vazirani, "NP is as easy as detecting unique solutions" but it involves randomized Turing reductions rather than the usual many-one reductions. —David Eppstein (talk) 18:41, 16 November 2008 (UTC)

text: I don't have time to work on this tonight, but in case anyone else wants to take a crack, I wrote more on this three years ago on my blog (usual disclaimers about reliable sources and original research go here). —David Eppstein (talk) 05:53, 17 November 2008 (UTC)

text: If each player has n choices, there are only n^2 pure strategy pairs to check, and each can be checked in linear time, so it's in P.  Finding a mixed strategy equilibrium is also in P, using linear programming.  I vaguely recall there was some related problem that was difficult (maybe finding ALL mixed strategy equilibria?)  —Preceding unsigned comment added by 75.173.217.183 (talk) 06:26, 19 November 2010 (UTC)

text: I checked the source for SMB and it seems legit. An instance of a 'problem' consists of a level, i.e. platforms, obstacles, etc. The question is whether it's possible for Mario to get from the start of the level to the end. The authors claim that certain other Nintendo games are NP-hard. RDBury (talk) 03:12, 8 August 2013 (UTC)
thread_title:  Games 

message: many of the problem titles in the section "spanning trees" which had no page seemed to be asking for the article []Steiner tree]] so I have directed them there. I am not certain that this is the best practice, but deleting them would likely lead to more confusion, and them being re-added later.
Jasen betts (talk) 10:02, 3 September 2009 (UTC)
thread_title:  Steiner tree 

message: Many of the problems in this list have no clear meaning.  It seems that a prerequisite for listing a problem here should be a reference: to a peer-reviewed paper, to a book, or at least to a wikipedia article.  —Preceding unsigned comment added by 132.64.44.156 (talk) 05:42, 15 August 2010 (UTC)
thread_title:  References 

message: Is there a website that features reductions used to prove hardness results, possibly using some graphical representation (i.e. edge-partitioning a graph is hard by reduction from 3SAT, which could be visualized by assigning vertex A to the former problem, vertex B to the latter, and directing an edge from B to A)? 134.58.42.46 (talk) 15:20, 20 October 2010 (UTC)
thread_title:  Actual reductions 

message: Non-trivial greatest common divisor links to Greatest common divisor of integers, which is clearly not np-hard. Euclids algorithm is a simple well known polynomial algorithm to compute the gcd.
This should be clarified or removed from the list.  — Preceding unsigned comment added by 46.14.248.115 (talk) 12:17, 20 December 2011 (UTC)
thread_title:  Non-trivial greatest common divisor 

message: It can be solved by Dijsktra's algorithm which runs in polynomial time. So was is it listed as an NP-complete problem?2001:760:3403:FFFC:2C63:181F:461E:6DE3 (talk) 15:44, 18 February 2013 (UTC)
thread_title:  Shortest path computation 

message: I find this NP-complete problem to be of a different flavor than others listed here. I think it should be included. It is discussed in the paper by Manders and Adelman, "NP-complete decision problems for Quadratic Polynomials".
The problem is incredibly simple. Given positive integers A,B,C \geq 0. Find positive integers
x,y such that Ax^2+By-C=0.
:I think it's rather A,B,C > 0. If A = 0, y = \frac{C}{B}, which is immediate. If B = 0, x = \sqrt{\frac{C}{A}}, which is immediate. If C = 0, x = 0 and y = 0. Morever, if y is positive, the problem is around O(min(\sqrt{\frac{C}{A}},\frac{C}{B})), which is not NP-complete. If y can be negative, I think the problem is more difficult than NP-complete as the entries are infinite. Ftiercel (talk) 16:28, 9 November 2016 (UTC)
replies: text:  Since this was recently (2019) added again, it is worth pointing out that 's comments here are totally wrong: the numbers  \sqrt{\frac{C}{A}}, \frac{C}{B} are exponential in the size of the input, so the naive algorithm implied by Ftiercel's comment runs in exponential time.  (To say nothing of ignoring what appears to be the perfectly valid citation that accompanied the addition.)  --JBL (talk) 14:53, 6 December 2019 (UTC)
thread_title:  Quadratic Polynomials 

message: Aren't you think that Traveling salesman problem & Bottleneck traveling salesman problem must be in Graphs and hypergraphs category?!!  — Preceding unsigned comment added by 41.248.23.77 (talk) 13:35, 8 July 2017 (UTC)
thread_title:  On TSP problems categorization 

message: The Art Gallery Problem was removed altogether from this article. This might be an easy solution, but I don’t find the article sufficiently informative this way.
Because there is a common misconception, that the standard version is NP-complete, it would be better to clarify which version is and which versions are not NP-complete.
My suggestion looks like this:
Art Gallery Problem with vertex guards (Other versions - where the placement of guards is allowed anywhere in the polygon or on the boundary - are ExiatentialReal complete <insert link to the article Existential theory of the reals>) 
I can’t provide a citation that the vertex guard version is not only NP-hard but also compete, because in older publications all versions are falsely labelled as NP-complete. And to anyone in the field it is clear, that this problem is in NP, if you only allow vertex guards. Can anyone back me on this or should I explain it quickly?
Also could someone else please post that edit if agreed upon? JRellek (talk) 23:58, 17 December 2019 (UTC)
replies: text: This is a list of NP-complete problems, not a list of problems that are complete for other classes that are hard for NP. It is indeed clear that it is in NP if you only allow vertex guards (you just have to cover all of the polynomially many regions of the visibility diagram of the candidate guard locations) but to include something like that we still need a source. Another problem here is that our art gallery article says nothing about NP-completeness of any variant. I think that problems listed here should go into more detail about the complexity in the linked article, and that is not currently true for this one. (It does discuss exists-R-completeness and NP-hardness, but not NP-completeness.) —David Eppstein (talk) 01:05, 18 December 2019 (UTC)
thread_title:  Art Gallery Problem 

message: I would like to add R1CS constraint system to the list. what do you think? Jackzhp (talk) 11:32, 14 March 2021 (UTC)
thread_title: R1CS constraint system

message: This is included in the list but I think it is wrong. I'm not sure about this but what is NP-Complete is the decision version, otherwise factoring should also be NP-complete (which most likely is not) as solving second degree Diophantine equations is equal to factoring. Alperen (talk) 17:21, 11 February 2023 (UTC)
replies: text: The first sentence of this list article is "This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems."  Does that address your concern?  --JBL (talk) 18:50, 11 February 2023 (UTC)
thread_title:  Solving two-variable quadratic polynomials over the integers