Winner Determination Algorithms for Graph Games with Matching Structures

Kanae Yoshiwatari, Hironori Kiya, Tesshu Hanaka, Hirotaka Ono

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

抄録

Cram, Domineering, and Arc Kayles are well-studied combinatorial games. They are interpreted as edge-selecting-type games on graphs, and the selected edges during a game form a matching. In this paper, we define a generalized game called Colored Arc Kayles, which includes these games. Colored Arc Kayles is played on a graph whose edges are colored in black, white, or gray, and black (resp., white) edges can be selected only by the black (resp., white) player, although gray edges can be selected by both black and white players. We first observe that the winner determination for Colored Arc Kayles can be done in O(2n) time by a simple algorithm, where n is the order of a graph. We then focus on the vertex cover number, which is linearly related to the number of turns, and show that Colored Arc Kayles, BW-Arc Kayles, and Arc Kayles are solved in time O∗(1.4143τ2+3.17τ), O∗(1.3161τ2+4τ), and O∗(1.1893τ2+6.34τ), respectively, where τ is the vertex cover number. Furthermore, we present an O((n/ ν+ 1 )ν) -time algorithm for Arc Kayles, where ν is neighborhood diversity. We finally show that Arc Kayles on trees can be solved in O(2n2) (= O(1. 4143n) ) time, which improves O(3n3) (= O(1. 4423n) ) by a direct adjustment of the analysis of Bodlaender et al.’s O(3n3) -time algorithm for Node Kayles.

本文言語英語
ホスト出版物のタイトルCombinatorial Algorithms - 33rd International Workshop, IWOCA 2022, Proceedings
編集者Cristina Bazgan, Henning Fernau
出版社Springer Science and Business Media Deutschland GmbH
ページ509-522
ページ数14
ISBN(印刷版)9783031066771
DOI
出版ステータス出版済み - 2022
イベント33rd International Workshop on Combinatorial Algorithms, IWOCA 2022 - Trier, ドイツ
継続期間: 6月 7 20226月 9 2022

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
13270 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

会議

会議33rd International Workshop on Combinatorial Algorithms, IWOCA 2022
国/地域ドイツ
CityTrier
Period6/7/226/9/22

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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