Algorithms for the maximum hamming distance problem

  • Authors:

  • Ola Angelsmark;Johan Thapper

  • Affiliations:

  • Department of Computer and Information Science, Linköpings Universitet, Linköping, Sweden;Department of Mathematics, Linköpings Universitet, Linköping, Sweden

  • Venue:
  • CSCLP'04 Proceedings of the 2004 joint ERCIM/CoLOGNET international conference on Recent Advances in Constraints
  • Year:
  • 2004

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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 $\mathcal{O}(1.7338^n)$ microstructure based algorithm for Max Hamming Distance 2-SAT, improving the previously best known algorithm for this problem, which has a running time of $\mathcal{O}(1.8409^n)$. We also give algorithms based on enumeration techniques for solving both Max Hamming Distancel-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 $\mathcal{O}(a^n)$ and (d,l)-CSP in $\mathcal{O}(b^n)$, then the corresponding Max Hamming problems can be solved in $\mathcal{O}((2a)^n)$ and $\mathcal{O}(b^n(1+b)^n)$, respectively.