After Cook’s paper [Coo71] published, Dick Karp immediately realized that the notion of NP-hardness captures a large amount of intractable combinatorial optimization problems. In [Kar72], he showed 21 problems to be NP-complete. This list quickly increased and by the time of 1979, Garey and Johnson [GJ79] wrote a whole book on NP-complete problems. This book has became a classic nowadays, and t...

This paper presents the differences between two NP problems. It focuses in the Euclidian 2 Dimension Travelling Salesman Problems and General Assign Problems. The main results are the triangle reduction to verify the solution in polynomial time for the former and for the later the solution to the Noted Conjecture of the NP-Class, NP is not P.

Tractability is the study of computational tasks with the goal of identifying which problem classes are tractable or, in other words, efficiently solvable. The class of tractable problems is traditionally assumed to be solvable in polynomial time by a deterministic Turing machine and is denoted by P. The class contains many natural tasks such as sorting a set of numbers, linear programming (the...

The inapproximability of non NP-hard optimization problems is investigated. Techniques are given to show that problems Log Dominating Set and Log Hypergraph Vertex Cover cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions are also approximable in deterministic subexponential time. A direct connection is established between non NP-hard problems...

We consider methods for constructing NP-intermediate problems under the assumption that P 6= NP. We generalize Ladner’s original method for obtaining NP-intermediate problems by using parameters with various characteristics. In particular, this generalization allows us to obtain new insights concerning the complexity of CSP problems. We begin by fully characterizing the problems that admit NP-i...