In this article we discuss the design of result veriication algorithms for optimization problems. In particular, we design time-optimal result veriication algorithms which verify the solution of all-pairs shortest paths, maximum-ow in a network, and matching problems. We prove that polynomial-time veriication algorithms for NP-complete problems do not exist exist, unless P = NP. Result veriicat...

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...

Finding approximate solutions to hard combinatorial optimization problems by neu-ral networks is a very attractive prospect. Many empirical studies have been done in the area. However, recent research about a neural network model indicates that for any NP-hard problem the existance of a polynomial size network that solves it implies that NP=co-NP, which is contrary to the well-known conjecture ...

the scheduling problems are the non-polynomial problems-hard (np-hard), is to solve it, and meta-heuristic innovative method compared with the exact method require less time and memory.in this research, developed imperialistic competitive algorithm used to solving the single-mode resource-constrained project scheduling problem.also the basic feasible solution algorithm used in order to increase...

How hard is it to invert NP-problems? We show that all superlinearly certified inverses of NP problems are coNP-hard. To do so, we develop a novel proof technique that builds diagonalizations against certificates directly into a circuit.