Result Verification Algorithms for Optimization Problems.

Abstract

In this article we discuss the design of result verification algorithms for optimization problems. In particular, we design time-optimal result verification algorithms which verify the solution of all-pairs shortest paths, maximum-flow in a network, and matching problems. We prove that polynomial-time verification algorithms for NP-complete problems do not exist exist, unless P = NP. Result verification problems for most of the NP-hard problems are not believed to be in NP. W e also consider verification algorithms for approximation algorithms for NP-complete and NP-hard problems.