social golfer problem and whist tournament

[fabio(Guest)]

Hi all,
I recently started to "play" on a tournament scheduling problem applied to tennis (I'm a tennis player and real fan) that I thought was new, but I was wrong since I discovered that is the Whist\\Bridge Tournament problem.

I found a connection of the Whist Scheduling Problem with the Social Golfer Problem since, for a specific family of players cardinalities a family of solutions of the Whist Problem are also solutions for the Social Golfer and vice versa (the Whist problem can be constructed in linear time starting from the Social Golfer problem solution).
What is interesting form me is that if a polynomial time algorithm exists for one of the two problems in this special case then the solution of the other problem can be derived in linear time.
As far as you know is this connection known? I wasn't able to find it out but as I was almost missing the Whist problem thus maybe that relation is known since many years.

Thank you in advance (and sorry for my English).

Fabio

[Ian Wakeling]

Hi Fabio,

I have moved your message here because replies are not possible in the comments area.

It true that you can take a Whist schedule and use it for golf foursomes, however pairs of players will play together 3 times, which, at a practical level, makes it larger than is necessary.  Indeed much of the literature on the golf problem deals only with the situation where players play together at most once.  For example have you seen this web page by Ed Pegg?

I am not sure of the connection you are referring to in your message (perhaps you could send me more details), but in general I would advise against trying to find general algorithms for these sort of combinatorial problems, as it is usually better to use combinatorics;  the last sentence from the link is wise advice indeed!

Ian.