@MISC{Gupta95resultverification, author = {Himanshu Gupta}, title = {Result Verification Algorithms for Optimization Problems}, year = {1995} }

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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. We also consider verification algorithms for approximation algorithms for NP-complete and NP-hard problems. 1 Introduction Consider a program A written to evaluate a function f. In this article we address the issue of being able to verify that the program A works correctly for all inputs i.e., A(x) = f(x) for all inputs x. Most of the approaches to this problem fall under the following broad categories: formal verification, program testing/checking and result verification. Formal verification of an algorithm or pro...