Polynomial transformations and data-independent neighborhood functions

Abstract

A neighborhood function that is polynomial in size and independent of the problem data, except that it may depend on the maximum absolute value of a number in an instance, is termed semi-reasonable. A semi-data-independent order transformation (SDIOT) is introduced such that if problem A SDIOT to problem B and B has a semi-reasonable neighborhood function, where the number of local optima is polynomial, then problem A has a semi-reasonable neighborhood function such that the number of local optima is polynomial. A large class of optimization problems is shown to SDIOT to Maximum Clause Weighted Satisfiability.