Linked Questions

102
votes
5answers
16k views

How not to solve P=NP?

There are lots of attempts at proving either $\mathsf{P} = \mathsf{NP} $ or $\mathsf{P} \neq \mathsf{NP}$, and naturally many people think about the question, having ideas for proving either direction....
50
votes
6answers
13k views

Why are some games np-complete?

I read the Wikipedia entry about "List of NP-complete problems" and found that games like super mario, pokemon, tetris or candy crush saga are np-complete. How can I imagine np-completeness of a game? ...
40
votes
3answers
4k views

Decision problems vs “real” problems that aren't yes-or-no

I read in many places that some problems are difficult to approximate (it is NP-hard to approximate them). But approximation is not a decision problem: the answer is a real number and not Yes or No. ...
40
votes
3answers
73k views

What exactly is polynomial time? [duplicate]

I'm trying to understand algorithm complexity, and a lot of algorithms are classified as polynomial. I couldn't find an exact definition anywhere. I assume it is the complexity that is not exponential....
29
votes
5answers
10k views

“NP-complete” optimization problems

I am slightly confused by some terminology I have encountered regarding the complexity of optimization problems. In an algorithms class, I had the large parsimony problem described as NP-complete. ...
24
votes
5answers
15k views

What is meant by “solvable by non deterministic algorithm in polynomial time” [duplicate]

In many textbooks NP problems are defined as: Set of all decision problems solvable by non deterministic algorithms in polynomial time I couldn't understand the part "solvable by non deterministic ...
23
votes
3answers
2k views

Why are NP-complete problems so different in terms of their approximation?

I'd like to begin the question by saying I'm a programmer, and I don't have a lot of background in complexity theory. One thing that I've noticed is that while many problems are NP-complete, when ...
16
votes
3answers
745 views

Is there a complexity viewpoint of Galois' theorem?

Galois's theorem effectively says that one cannot express the roots of a polynomial of degree >= 5 using rational functions of coefficients and radicals - can't this be read to be saying that given a ...
14
votes
5answers
6k views

Flaw in my NP = CoNP Proof?

I have this very simple "proof" for NP = CoNP and I think I did something wrongly somewhere, but I cannot find what is wrong. Can someone help me out? Let A be some problem in NP, and let M be the ...
14
votes
1answer
295 views

How can you bound the error of an approximation without knowing the optimal solution?

I been looking at this site and it says that people found solutions for TSP tours that are just 0.031% higher than the optimal tour is. Without finding the optimal tour how does they know what length ...
13
votes
3answers
5k views

P, NP and specialised Turing Machines

I'm sort of new, but very interested to the field of computing and complexity theory, and I want to clarify my understanding about how to class problems, and how strongly the problems relate to the ...
10
votes
2answers
5k views

Do any decision problems exist outside NP and NP-Hard?

This question asks about NP-hard problems that are not NP-complete. I'm wondering if there exist any decision problems that are neither NP nor NP-hard. In order to be in NP, problems have to have a ...
10
votes
2answers
363 views

Combinatory interpretation of lambda calculus

According to Peter Selinger, The Lambda Calculus is Algebraic (PDF). Early in this article he says: The combinatory interpretation of the lambda calculus is known to be imperfect, because it does ...
8
votes
2answers
2k views

Simple graph canonization algorithm

I'm looking for an algorithm that provides a canonical string for a given colored graph. Ie. an algorithm that returns a string for a graph, such that two graphs get the same string if and only if ...
8
votes
1answer
532 views

Relaxed Bin Packing Problem

The problem I have is like this bin packing problem, but instead I have $n$ bins and a collection of items with discrete masses. I need to put at least $m$ kg of stuff in each bin. Is there an ...

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