Sorting a sequence of strong kings in a tournament

  • Authors:

  • Ting-Yem Ho;Jou-Ming Chang

  • Affiliations:

  • Department of Public Finance and Tax Administration, National Taipei College of Business, Taipei, Taiwan 10021;Department of Information Management, National Taipei College of Business, Taipei, Taiwan 10021

  • Venue:
  • Information Processing Letters
  • Year:
  • 2003

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Abstract

A king in a tournament is a player who beats any other player directly or indirectly. According to the existence of a king in every tournament, Wu and Sheng [Inform. Process. Lett. 79 (2001) 297-299] recently presented an algorithm for finding a sorted sequence of kings in a tournament of size n, i.e., a sequence of players u1, u2,....,un such that ui → ui+1 (ui beats ui+1) and ui is a king in the sub-tournament induced by {ui, ui+1,.....,un} for each i = 1, 2,....,n - 1. With each pair u,v of players in a tournament, let b(u,v) denote the number of third players used for u to beat v indirectly. Then, a king u is called a strong king if the following condition is fulfilled: if v → u then b(u, v) b(v,u). In the sequel, we will show that the algorithm proposed by Wu and Sheng indeed generates a sorted sequence of strong kings, which is more restricted than the previous one.