Algorithms for the Maximum Hamming Distance Problem

  • Ola Angelsmark
  • Johan Thapper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3419)


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 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 \(\mathcal{O}(a^n)\) 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ola Angelsmark
    • 1
  • Johan Thapper
    • 2
  1. 1.Department of Computer and Information ScienceLinköpings UniversitetLinköpingSweden
  2. 2.Department of MathematicsLinköpings UniversitetLinköpingSweden

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