Some simplified NP-complete graph problems

The P versus NP-complete dichotomy of some challenging problems in graph theory

Checking for optimal solutions in some NP-complete problems.

For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their ze...

On the Locality of Some NP-Complete Problems

We consider the distributed message-passing LOCAL model. In this model a communication network is represented by a graph where vertices host processors, and communication is performed over the edges. Computation proceeds in synchronous rounds. The running time of an algorithm is the number of rounds from the beginning until all vertices terminate. Local computation is free. An algorithm is call...

Simplified Harvest Moon is NP-Complete

Recently, some significant work has been done to analyze the complexity class of classic electronic games. In these works, the rules of the game are generalized and then the generalized games are classified by formulating them as a decision problem and reducing them to a problem known to be NP-complete [1, 2]. We use a similar approach to prove the complexity class of a particular class of mode...

A Simplified NP-Complete MAXSAT Problem

It is shown that the MAX2SAT problem is NP-complete even if every variable appears in at most three clauses. However, if every variable appears in at most two clauses, it is shown that it (and even the general MAXSAT problem) can be solved in linear time. When every variable appears in at most three clauses, we give an exact algorithm for MAXSAT that takes at most O(3 n=2 n) steps where n is th...