Volume 10, Number 1, 7-21, DOI: 10.1007/s10601-004-5305-9

Solving Kirkman’s Schoolgirl Problem in a Few Seconds

Nicolas Barnier and Pascal Brisset

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Abstract

The Social Golfer Problem has been extensively used by the constraint community in recent years as an example of a highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right model for one problem. We address in this paper a specific instance of the Golfer Problem well known as Kirkmanrsquos Schoolgirl Problem and list a collection of techniques and tricks to find efficiently all its unique solutions. In particular, we propose SBDD+, a generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques improves previously published results by an order of magnitude for CPU time as well as for number of backtracks. It computes the seven unique solutions of Kirkmanrsquos problem in a few seconds.

Keywords  symmetry breaking - social golfer problem - resolvable steiner systems

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