Scheduling a Major College Basketball Conference—Revisited

Abstract

Nemhauser and Trick presented the problem of finding a timetable for the 1997/98 Atlantic Coast Conference (ACC) in basketball. Their solution, found with a combination of integer programming and exhaustive enumeration, was accepted by the ACC. Finite-domain constraint programming is another programming technique that can be used for solving combinatorial search problems such as sports tournament scheduling. This paper presents a solution of round robin tournament planning based on finite-domain constraint programming. The approach yields a dramatic performance improvement, which makes an integrated interactive software solution feasible.

Global constraints for round robin tournament scheduling

“…However, we are here mainly concerned with consistency techniques. For the other aspects of constraint-based round robin scheduling, see [7,8].…”

“…Most previous work on constraint-based tournament planning [19,11,8,7] used only algorithm 1 for the all-different constraint and algorithm 1 for the one-factor constraint. Trick [22] suggests to use algorithm 2 for the all-different constraint and algorithm 2 for the one-factor constraint.…”

“…We consider the problem of finding all schedules that minimize the overall number of breaks. A widely accepted method of searching for intermural tournaments is to generate pattern sets first [20,15,7,8]. These are sets of home/away patterns that satisfy simple row and column constraints [7].…”

“…Table 3 shows the run times for finding all solutions of intermural tournament problems, all of which except the last one are randomly constrained as in the previous section. The last problem is the ACC 1997/98 problem [15,8], which is tightly constrained by a variety of conditions. Since we are not concerned with the computation of the pattern sets, we fix a particular pattern set for the benchmarks, except for the ACC 1997/98 problem.…”

“…Techniques that have been used to solve such problems include integer programming [20,15], local search [24] and constraint programming [19,11,7]. Constraint programming has been shown recently to outperform integer programming on practical problems [8,7]. Constraint programming allows to systematically exploit the round robin and other constraints, often leading to relatively small search trees for medium-sized tournaments.…”