Sport tournament planning becomes a complex task in the presence of heterogeneous requirements from teams, media, fans and other parties. Existing approaches to sport tournament planning often rely on precomputed tournament schemes which may be too rigid to cater for these requirements. Existing work on sport tournaments suggests a separation of the planning process into three phases. In this work, it is shown that all three phases can be solved using finite-domain constraint programming. The design of Friar Tuck, a generic constraint-based round robin planning tool, is outlined. New numerical results on round robin tournaments obtained with Friar Tuck underline the potential of constraints over finite domains in this area. i Introduction

In a sport competition, n given teams play against each other over a period of time according to a certain scheme. The round robin scheme is popular in many team sports like football and basketball. It determines that every team t plays against every other team a fixed number of times r during the competition. If r is 1, the scheme is called single round robin, and if r is 2, it is called double round robin. The matches take place at one of the opponents' facilities. If a team uses its own facilities in a match, it is said to have a home match, otherwise it has an away match. This paper focuses on temporally dense round robin tournaments (abbreviáted as RR throughout the paper), in which the rn (n-1)/2 matches are distributed over a minimal number d of dates such that every team plays at most one match per date. If n is even, d is r (n-1). k RR with an odd number of teams consists of ro dates in each of which n-i teams play and one team does not. This team is said to have a bye. Table i shows a RR for n= 5 and r= 1. The integral value in row t and column j tells the team against which team t plays in date j: the+ or-symbol indicates that the match is a home match or an away match, respectively, for team f; and b indicates a bye. A similar notation is used by Schreuder [16] and Russell and Leung [14]. This basic setup can be refined by additional requirements in various ways. The following list contains common requirements in tournament plan-fling practice.