Many real world problems are over-constrained, but with hard constraints which must be satisfied. For such problems we define Max-A-CSP, in which we search for maximal partial assignments which violate no constraints over assigned variables. We develop a branch-and-bound algorithm which interleaves arc consistency maintenance with reasoning about unassigned variables. We show that the unassigned variables make it difficult to find effective lower bounds. Finally, we test the algorithm on random binary constraint problems, comparing it to a version of forward checking, and show that, as for CSPs, the extra consistency maintenance improves performance on hard sparse problems.


Constraint Satisfaction Problem Soft Constraint Partial Assignment Sparse Problem Future Variable 
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Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • Ken Brown
    • 1
  1. 1.Cork Constraint Computation Centre, Department of Computer ScienceUniversity College CorkIreland

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