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Abstract

Arc-consistency algorithms are the workhorse of backtrackers that Maintain Arc-Consistency (MAC). This paper provides experimental evidence that, despite common belief to the contrary, it is not always necessary for a good arc-consistency algorithm to have an optimal worst case time-complexity. To sacrifice this optimality allows MAC solvers that (1) do not need additional data structures during search, (2) have an excellent average time-complexity,and (3) have a space-complexity that improves significantly on that of MAC solvers that do have optimal arc-consistency components. Results are presented from an experimental comparison between MAC-2001, MAC-3 d and related algorithms. MAC-2001 has an arc-consistency component with an optimal worst case time-complexity, whereas MAC-3 d has not. MAC-2001 requires additional data structures during search, whereas MAC-3 d does not. MAC-3d has a space-complexity of O(e + nd), where n is the number of variables, d the maximum domain size, and e the number of constraints. We demonstrate that MAC-2001’s space-complexity is O(ed min(n, d)). MAC-2001 required about 35% more average solution time than MAC-3 d for easy and hard random problems and MAC-3 d was the quickest algorithm to solve 23 out of 25 real-world problems, and was only marginally slower for the remaining 2. This indicates that lightweight algorithms like MAC-3 d are promising, especially if checks are cheap and memory is scarce.

Keywords

Problem Size Constraint Satisfaction Problem Selection Heuristic Random Problem Free Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • M. R. C. van Dongen
    • 1
  1. 1.Cork Constraint Computation Centre, Computer Science DepartmentUniversity College CorkIreland

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