Algorithms for the MAXIMUM HAMMING DISTANCE problem

Abstract

We study the problem of finding two solutions to a constraint satisfaction problem which differ on the assignment of as many variables as possible - the MAX HAMMING DISTANCE problem for CSPs - a problem which can, among other things, be seen as a domain independent way of quantifying "ignorance." The first algorithm we present is an Ο(1.7338n) microstructure based algorithm for MAX HAMMING DISTANCE 2-SAT, improving the previously best known algorithm for this problem, which has a running time of Ο(1.8409n). We also give algorithms based on enumeration techniques for solving both MAX HAMMING DISTANCE l-SAT, and the general MAX HAMMING DISTANCE (d, l)-CSP, the first non-trivial algorithms for these problems. The main results here are that if we can solve l-SAT in Ο(an) and (d,l)-CSP in Ο(bn), then the corresponding Max Hamming problems can be solved in Ο((2a)n) and Ο(bn(1 + b)n), respectively. © Springer-Verlag Berlin Heidelberg 2005.