Eleme Turnuvalarında Seribaşı Eşlemelerinin Sayılması ve Sayımlanması

Öz

Eleme turnuvaları, yarışma tasarımlarının muhtemelen en yaygın olarak kullanılanıdır. Bu turnuvalarda, her turda tüm yarışmacılar bir eleme karşılaşması oynamak üzere eşlenirler ve kaybeden turnuva dışında kalır. Seribaşı eşlemesi olarak adlandırılan ilk tur maçlarının seçimi, turnuvanın geri kalanını da doğrudan etkiler. Seribaşı eşlemelerini çeşitli açılardan değerlendiren ve inceleyen, dikkate değer sayıda çalışma olmasına karşın, bildiğimiz kadarıyla seribaşı eşlemelerini sayımlayan bir algoritma sunulmamıştır. Ayrıca, literatürde farklı seribaşı eşlemelerinin sayısının bulunması da yalnızca kısaca tartışılmıştır. Bu makalede farklı seribaşı eşlemelerinin nasıl sayılacağı tartışılmış ve eleme turnuvalarında seribaşı eşlemelerinin sayımlanması için etkin bir algoritma önerilmiştir.

Anahtar Kelimeler

• Hesaplamalı Turnuva Tasarımı
• Eleme Turnuvası
• Seribaşı Eşleme
• Sayma
• Sayımlama

Counting and Enumerating Seedings in Knockout Tournaments

Öz

Knockout tournaments are probably the most common of all competition designs. In those tournaments, all competitors are paired to play an elimination match at each round, where the loser is immediately knocked out of the tournament. The setting of the first round of matches, named as seeding, directly influences the rest of the tournament. While there is a considerable amount of work that evaluate and examine different seedings from various perspectives, an algorithm that enumerates seedings has not been given to the best of our knowledge. Also, counting the number of unique seedings has been only briefly discussed in the literature. This paper discusses how to count the number of unique seedings and proposes an efficient algorithm for enumerating seedings in a knockout tournament.

Anahtar Kelimeler

• Computational Tournament Design
• Knockout Tournament
• Seeding
• Counting
• Enumeration

Kaynakça

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