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Questions related to the (computational) complexity of solving problems

7
votes
As pointed out by @Vor the point of polynomial-time reductions is to show that if have a reduction from A to B and an algorithm to solve a problem B then you can use it to efficiently (i.e. in polynom …
answered Oct 8 '12 by Artem Kaznatcheev
8
votes
First of all, these are not subproblems but different types of problems. In one your promise me that $n/2$ of the clauses only have 2 literals, and in the other your promise me that only $\log n$ of t …
answered Mar 3 '14 by Artem Kaznatcheev
13
votes
2answers
Suppose I have a graph $G$ with $M(G)$ the (unknown) set of perfect matchings of $G$. Suppose this set is non-empty, then how difficult is it to sample uniformly at random from $M(G)$? What if I am ok …
asked Mar 24 '13 by Artem Kaznatcheev
6
votes
Although you already know from the other answers that the question is solvable in polynomial time, I thought I would expand on the computational complexity of reachability since you used complexity te …
answered Feb 6 '14 by Artem Kaznatcheev
11
votes
As @Kaveh stated, this question is only interesting if we assume $P \neq NP$; the rest of my answer takes this as an assumption, and mostly provides links to further wet your appetite. Under that assu …
answered May 12 '12 by Artem Kaznatcheev
27
votes
3answers
Given an instance of SAT, I would like to be able to estimate how difficult it will be to solve the instance. One way is to run existing solvers, but that kind of defeats the purpose of estimating di …
asked Mar 15 '12 by Artem Kaznatcheev
11
votes
1answer
Modern SAT-solvers are very good at solving many real-world examples of SAT instances. However, we know how to generate hard ones: for instance use a reduction from factoring to SAT and give the RSA n …
asked Jul 22 '12 by Artem Kaznatcheev
26
votes
I think you misunderstood what it means to solve a diophantine equation, and Matiyasevich's indecidability theorem. Matiyasevich proved that for every RE set $S$ there is a diophentine equation $f(n; …
answered May 17 '12 by Artem Kaznatcheev
17
votes
1answer
My goal is to solve the following problem, which I have described by its input and output: Input: A directed acyclic graph $G$ with $m$ nodes, $n$ sources, and $1$ sink ($m > n \geq 1$). Output: T …
asked Apr 25 '12 by Artem Kaznatcheev