Redundant Modeling for the QuasiGroup Completion Problem

Abstract

The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, and the focus of much recent interest in the area of constraint programming. [5] reports that QCPs of order 40 could not be solved by pure constraint programming approaches, but could sometimes be solved by hybrid approaches combining constraint programming with mixed integer programming techniques from operations research. In this paper, we show that the pure constraint satisfaction approach can solve many problems of order 45 in the transition phase, which corresponds to the peak of difficulty. Our solution combines a number of known ideas -the use of redundant modeling [3] with primal and dual models of the problem connected by channeling constraints [13] - with some novel aspects, as well as a new and very effective value ordering heuristic. © Springer-Verlag 2003.