Recent Advances in Constraints

Volume 3419 of the series Lecture Notes in Computer Science pp 41-55

Trying Again to Fail-First

  • J. Christopher BeckAffiliated withDepartment of Mechanical & Industrial Engineering, University of Toronto
  • , Patrick ProsserAffiliated withDepartment of Computer Science, University of Glasgow
  • , Richard J. WallaceAffiliated withCork Constraint Computation Center and Department of Computer Science, University College Cork

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For constraint satisfaction problems (CSPs), Haralick & Elliott [1] introduced the Fail-First Principle and defined in it terms of minimizing branch depth. By devising a range of variable ordering heuristics, each in turn trying harder to fail first, Smith & Grant [2] showed that adherence to this strategy does not guarantee reduction in search effort. The present work builds on Smith & Grant. It benefits from the development of a new framework for characterizing heuristic performance that defines two policies, one concerned with enhancing the likelihood of correctly extending a partial solution, the other with minimizing the effort to prove insolubility. The Fail-First Principle can be restated as calling for adherence to the second, fail-first policy, while discounting the other, promise policy. Our work corrects some deficiencies in the work of Smith & Grant, and goes on to confirm their finding that the Fail-First Principle, as originally defined, is insufficient. We then show that adherence to the fail-first policy must be measured in terms of size of insoluble subtrees, not branch depth. We also show that for soluble problems, both policies must be considered in evaluating heuristic performance. Hence, even in its proper form the Fail-First Principle is insufficient. We also show that the “FF” series of heuristics devised by Smith & Grant is a powerful tool for evaluating heuristic performance, including the subtle relations between heuristic features and adherence to a policy.