Polynomial transformations and data-independent neighborhood functions

Authors:
Derek E. Armstrong;Sheldon H. Jacobson
Affiliations:
Alphatech, Inc., 3811 North Fairfax Drive, Arlington, VA;Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL
Venue:
Discrete Applied Mathematics
Year:
2004

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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.