A bracket assignment problem for the National Collegiate Athletic Association Men's Basketball Tournament

Abstract

The National Collegiate Athletic Association Men's Basketball Tournament is a 65-team championship in American college basketball, in which a single team is eliminated in a play-in game, followed by a six-round, single-elimination tournament. Owing to its immense popularity, each aspect of the tournament, including the selection of teams, their ranking (or “seeding”), and the assignment of teams to locations for the first few rounds, is a hotly debated topic. In this paper, we concentrate on the latter aspect of the tournament composition, as the first two elements have been extensively researched in a variety of settings. We formulate the team assignment problem as a mixed-integer program, and examine various methods of tightening the linear programming relaxation in order to yield an effective methodology for generating feasible tournament pairings with minimum expected travel. Finally, we demonstrate the results of our algorithm on data derived from the 2004 and 2005 basketball tournaments.