From: rogerlee@leland.Stanford.EDU (Roger W Lee) Subject: Re: Round robins in multiple venues Date: 17 Feb 1999 19:45:35 -0800 Newsgroups: sci.math.research Keywords: balanced tournament designs In article <7af6op$it0$1@nnrp1.dejanews.com>, Michael Albert wrote: >Schedule a complete round robin among 2k participants at k sites (all used >simultaneously in each round) in such a way that for each participant her >(2k-1) matches find her visiting (k-1) sites twice, and one site once. You're looking for a "balanced tournament design" (BTD). >2) It's easy enough to find schedules which work for small numbers of >participants (4 is easily proven impossible, there's a cute one for 6 based >on sums of particpant numbers mod 3, and several less nice ones for 8.) As >well as wanting to have practical examples to hand I'd be interested in any >tricks or techniques which sometimes work. And of course as a mathematician >I'd be most interested of all in a theorem, particularly if accompanied by an >algorithm. A BTD exists for all k not equal to 2. For k congruent to 0 or 1 (mod 3), see J. Haselgrove and J. Leech, A tournament design problem, Amer. Math. Monthly 84 (1977) 198-201. For k congruent to 2 (mod 3), see P.J. Schellenberg, G.H.J. van Rees, and S.A. Vanstone, The existence of balanced tournament designs, Ars Combin. 3 (1977) 303-318. -Roger