The scaling of search cost

Authors:
Ian P. Gent;Ewan MacIntyre;Patrick Prosser;Toby Walsh
Affiliations:
Department of Computer Science, University of Strathclyde, Glasgow, Scotland;Department of Computer Science, University of Strathclyde, Glasgow, Scotland;Department of Computer Science, University of Strathclyde, Glasgow, Scotland;Department of Computer Science, University of Strathclyde, Glasgow, Scotland
Venue:
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Year:
1997

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Abstract

We show that a rescaled constrainedness parameter provides the basis for accurate numerical models of search cost for both backtracking and local search algorithms. In the past, the scaling of performance has been restricted to critically constrained problems at the phase transition. Here, we show how to extend models of search cost to the full width of the phase transition. This enables the direct comparison of algorithms on both under-constrained and over-constrained problems. We illustrate the generality of the approach using three different problem domains (satisfiability, constraint satisfaction and travelling salesperson problems) with both backtracking algorithms like the Davis-Putnam procedure and local search algorithms like GSAT. As well as modelling data from experiments, we give accurate predictions for results beyond the range of the experiments.