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n Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie - Skedulering van gade-vermydende gemengdedubbels rondomtalie-tennistoernooie : navorsing- en oorsigartikels

Volume 28, Issue 1
  • ISSN : 0254-3486
  • E-ISSN: 2222-4173

Abstract

By die opstel van 'n gade-vermydende gemengde-dubbels rondomtalie-tennistoernooi van orde word daar gesoek na 'n spelskedule waarvolgens getroude pare op só 'n manier in gemengde-dubbels tennispotte kragte meet dat geen speler saam met sy / haar eggenoot in 'n span afgepaar word nie, geen speler teen sy / haar eggenoot te staan kom nie, elke speler presies een keer teen elke ander speler van dieselfde geslag te staan kom, elke speler presies een keer saam met elke speler van die teenoorgestelde geslag (behalwe sy / haar gade) in 'n span afgepaar word, en elke speler presies een keer teen elke speler van die teenoorgestelde geslag (behalwe sy / haar gade) te staan kom. Hierdie potte moet boonop in die kleinste moontlike aantal rondtes ingedeel word sodat geen speler in meer as een pot per rondte meeding nie, en sodat die aantal potte per rondte dieselfde en 'n maksimum is. Spelskedules vir sulke toernooie word vir ≤ 20 opgestel en ter wille van naslaandoeleindes op 'n gebruikersvriendelike manier gedokumenteer.


The problem of scheduling a spouse-avoiding mixed doubles round-robin tennis tournament (SMDRTT) of order involves finding a playing schedule for married couples in such a way that no player teams up with his / her spouse, no player opposes his / her spouse, each player opposes every other player of the same sex exactly once, each player teams up with every player of the opposite sex (except his / her spouse) exactly once, and each player opposes every player of the opposite sex (except his / her spouse) exactly once. These mixed doubles tennis matches have to be partitioned into the smallest number of rounds so that no player plays more than once per round and so that each round comprises the maximum number of matches. If is even, then each player may be scheduled to compete in every round and hence an SMDRTT of even order comprises -1 rounds, each containing / 2 matches. However, if is odd, then one man and one woman must necessarily receive a bye during each round and hence an SMDRTT of odd order comprises rounds, each containing ( - 1) / 2 matches.
The notion of an SMDRTT may be attributed to the director of the Briarcliff Racquet Club in New York, who sought such a schedule for his club in 1972. His motivation was that spouses know each other too well and hence may have an unfair advantage with respect to anticipating elements in each other's play. Although it is known that results from the mathematical subdiscipline of design theory may be used to construct SMDRTTs of virtually any order, neither these techniques nor the application thereof is easily accessible to administrators of tennis clubs, who are typically not mathematicians. The aim in this paper is therefore two-fold:
  1. (I) to investigate which techniques from design theory are applicable in the construction of playing schedules for SMDRTTs, and
  2. (II) to apply these techniques in the construction of playing schedules for SMDRTTs of order ≤ 20, and to document the resulting schedules in a way that is easily accessible to non-mathematicians.

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/content/aknat/28/1/EJC20443
2009-12-01
2019-08-24

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