Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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On January 5, 1996, Maariv, one of the two leading daily newspapers in Israel, announced ''The Dream League'' game. Every participant in this game was required to ''purchase'' from a pool of all the soccer players in the Israeli National League, a team which according to his judgment would be chosen as the best team at the end of the season. Purchasing the players was subject to a given budget and to several other constraints. After the soccer season was over, we were requested by Maariv to find the optimal ''Dream Team''. The problem of finding the optimal team is shown to be a generalized version of the well-known knapsack problem. It is formulated as an integer program and solved to optimality by the software NAG. Evidently, the optimal Dream Team is much better (in terms of the total cumulative grade) than the actual winning team chosen by the readers of Maariv. A possible heuristic procedure for solving the game in larger settings is also discussed.