Questions tagged [np-complete]

Questions on the topic of NP-Completeness, which comes from Theoretical Computer Science

620 questions
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What is the $3$-SAT problem?

In the hopes of improving my knowledge on the question, could someone outline the inputs and outputs for the 3-SAT problem? It would also be helpful if you could express how this problem differs in structure to SAT, 2-SAT or 4-SAT problems.
nubela
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Simple "real life" NP-hard problems?

There are many proofs lying around that games like Lemmings or Sudoku or Tetris are NP-hard (generalized version of those games, of course). The proofs, as I recall, are not difficult but not simple either. I wish to give my students a question in…
Gadi A
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Why are there only a few known Ramsey numbers?

Can someone explain in a simple way why there are so few known exact Ramsey numbers? I guess it's because there are no efficient algorithms for this task, but are there so many combinations to test? And an additional question: How are the bounds…
Fred Funks
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What are NP-complete problems and why are they so important?

I keep hearing questions about whether something is NP-complete, but they never really mention what it is. Why do people care so much about NP-complete problems?
Gordon Gustafson
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What is the complexity of succinct (binary) Nurikabe?

Nurikabe is a constraint-based grid-filling puzzle, loosely similar to Minesweeper/Nonograms; numbers are placed on a grid to be filled with on/off values for each cell, with each number indicating a region of connected 'on' cells of that size, and…
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Solving SAT by converting to disjunctive normal form

The first well-known $NPC$ problem is the Boolean Satisfiability Problem, which has a proof of being $NPC$ done by Cook (Cook-Levin Theorem). The problem can easily be described the following way: In complexity theory, the satisfiability problem…
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Must an algorithm that decides a problem in NP also produce a solution?

I think I have a basic misunderstanding in the definition of a decision problem. It's widely believed that a constructive proof of P=NP with a practical implementation would break all modern cryptography, for…
user256439
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The practical implication of P vs NP problem

Although whether $$ P = NP $$ is important from theoretical computer science point of view, but I fail to see any practical implication of it. Suppose that we can prove all questions that can be verified in polynomial time have polynomial time…
Graviton
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Example of a problem that is NP-Hard but not NP-Complete

Please, mention one problem that is NP-Hard but not NP-Complete? And, explain why. I see some papers assert Degree Constrained Minimum Spanning Tree is an NP-Hard problem and some say it's NP-Complete. Why so? Is it something that we don't have a…
user1869
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How would you input xkcd.com/287 into WolframAlpha?

In this XKCD comic, a stick figure asks an NP-complete problem to order exactly 15.05 worth of appetizers out of a menu that includes the following list of prices: {2.15, 2.75, 3.35, 3.55, 4.20, 5.80}. What is the mathematical name and procedure for…
Evgeny
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Arranging a set of strings to form a palindrome: NP complete?

Is it NP complete to determine if a given set of strings can be arranged to form a palindrome? Example: The strings {"German" "man" "am" "am" "I" "I" "regal" "a"} can be arranged into "I man am regal a German am I". The strings {"bat" "bat"} cannot…
user253970
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Is finding the length of the shortest addition chain for a number $n$ really $NP$-hard?

I spent a few hours today working through the addition chain problem. Given the starting number 1, how many additions are required to get to some target natural number n? For example, to make 5, we need three additions: 1 + 1 = 2 2 + 2 = 4 4 + 1…
templatetypedef
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Is it possible that P != NP cannot be proved?

I am probably asking a stupid question but what I gather from a layman explanation of Godel's incompleteness theorem is that it is completely possible that a true statement cannot be derived from theorem and axioms. While all evidence points out…
user114370
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Assuming $P \neq NP$, do we know whether there are problems which are in $NP$, not in $P$ and are not $NP$ complete?

Here's a question. Have there been any theoretical results showing that if $P \neq NP$, there must exist some problems in $NP$ which are not $NP$-complete and which are not in $P$ either? Just curious because I've never seen this question…
ted
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A graph problem

Consider the following graph problem. For a number $K$ and a set $\mathcal{K} = \{ 1, \ldots,K\}$, we have a set of vertices $V_k^s$ for all $s \subset \mathcal{K} \setminus \{k\}$, $s$ is not empty and for all $k$. For example, if $K =2$, we have…
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