any expert could help me why this sentence is True? if L ∈ NP and L ≤p 3−SAT (i.e: reduce L to 3-SAT in poly time) then L is NP-Complete. ...

First of all, I want to mention that this is my homework. However, to solve my problem I can use any literature I want. Even though I think that problem is clear from its name, I will give it description: "For given undirected graph G and given integer k, does...

This is a homework assignment, so any help is appreciated. I should prove that the following problem is NP-complete. The hint says that you should reduce the subset sum problem to this problem. Given a set of shapes, like the below, and an m-by-n board, decide whether is it possible...

The MWIS (Maximum weight independent set) is a NP-complete problem, so if P!=NP we cannot find a solution in a good enough time complexity. I am looking for an algorithm that can find an approximation of the MWIS in an arbitrary graph within a good time complexity. I am currently...

This problem is similar to the "Exact Hitting Set" problem (http://en.wikipedia.org/wiki/Exact_cover#Exact_hitting_set) but with slightly different constraints. I am looking for libraries, implementations, or papers that solve the following. Say I have a set of sets S, and is initialized as follows: S = {N, O, P, E}; N = {1,...