Improving Bounds on the Football Pool Problem by Integer Programming and High-Throughput Computing

Authors:
Jeff Linderoth;François Margot;Greg Thain
Affiliations:
Department of Industrial and Systems Engineering, University of Wisconsin--Madison, Madison, Wisconsin 53706;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Department of Computer Science, University of Wisconsin--Madison, Madison, Wisconsin 53706
Venue:
INFORMS Journal on Computing
Year:
2009

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Abstract

The football pool problem, which gets its name from a lottery-type game where participants predict the outcome of soccer matches, is to determine the smallest covering code of radius 1 of ternary words of length v. For v = 6, the optimal solution is not known. Using a combination of isomorphism pruning, subcode enumeration, and linear programming-based bounding, running on a high-throughput computational grid consisting of thousands of processors, we are able to improve the lower bound on the size of the optimal code from 65 to 71.