User michael - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T04:45:16Z http://mathoverflow.net/feeds/user/14241 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61165/generating-fixtures-for-a-chess-league-with-a-twist Generating fixtures for a chess league, with a twist Michael 2011-04-09T21:34:23Z 2011-04-10T12:13:14Z <p>Hello,</p> <p>I am in the process of building some software to generate fixtures for a <a href="http://michaelfraser.me/" rel="nofollow">chess</a> league. Which has a little twist which complicates matters. I would like to introduce a constraint. Where by a team and the below team from a club are not allowed to play on the same night. e.g. Loughborough 1 is not allowed to play on the same night as Loughborough 2. This help teams share players, therefore play more games.</p> <p>The league has five divisions, with 8, 7, 8, 7, 7 teams in respectively. The first half of the league is played over 10 weeks. This means that teams do not have to play each week.</p> <p>A solution would be to brute force all the fixture combinations, for all the divisions. The problem with this approach is that there are way too many combinations!</p> <p>I am wondering if there are any mathematical techniques that I could use to help me with this problem. I am not wanting to find a unique solution (a combination of fixtures, without violating the constraints). I would be happy with an algorithm which produced 10 violation of constraints in the season.</p> <p>Any help or pointers would be greatly appreciated.</p> <p>Can you suggest any areas for me to research.</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/61165/generating-fixtures-for-a-chess-league-with-a-twist/61205#61205 Comment by Michael Michael 2011-04-13T18:03:34Z 2011-04-13T18:03:34Z Thanks for the interesting ideas. This approach would be similar to how the person manually does it. I have hunted around for some material on these ideas. I will report back once I have a grasp of it. http://mathoverflow.net/questions/61165/generating-fixtures-for-a-chess-league-with-a-twist Comment by Michael Michael 2011-04-10T09:52:31Z 2011-04-10T09:52:31Z I have undertaken this challenge as I see it as interesting cross between computer science and mathematics. I haven't done any mathematical programming since the days of my degree. At this stage in my question. I would be really happy if someone would say, go and take a look at x, y, z branch of mathematics. http://mathoverflow.net/questions/61165/generating-fixtures-for-a-chess-league-with-a-twist Comment by Michael Michael 2011-04-10T09:49:00Z 2011-04-10T09:49:00Z I am not a regular user of forums. Forgive me for not understanding the protocol. In hindsight, I do consider it impolite to post in two forums. I will certainly not make this mistake in the future. There doesn't seem an obvious way for me to close the question in the second site that I asked in.