From Donkeys to Kings in Tournaments

Amir Abboud, Tomer Grossman, Moni Naor, Tomer Solomon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A tournament is an orientation of a complete graph. A vertex that can reach every other vertex within two steps is called a king. We study the complexity of finding k kings in a tournament graph. We show that the randomized query complexity of finding k ≤ 3 kings is O(n), and for the deterministic case it takes the same amount of queries (up to a constant) as finding a single king (the best known deterministic algorithm makes O(n3/2) queries). On the other hand, we show that finding k ≥ 4 kings requires Ω(n2) queries, even in the randomized case. We consider the RAM model for k ≥ 4. We show an algorithm that finds k kings in time O(kn2), which is optimal for constant values of k. Alternatively, one can also find k ≥ 4 kings in time nω (the time for matrix multiplication). We provide evidence that this is optimal for large k by suggesting a fine-grained reduction from a variant of the triangle detection problem.

Original languageEnglish
Title of host publication32nd Annual European Symposium on Algorithms, ESA 2024
EditorsTimothy Chan, Johannes Fischer, John Iacono, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages14
ISBN (Electronic)9783959773386
DOIs
StatePublished - 23 Sep 2024
Event32nd Annual European Symposium on Algorithms, ESA 2024 - London, United Kingdom
Duration: 2 Sep 20244 Sep 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume308
ISSN (Print)1868-8969

Conference

Conference32nd Annual European Symposium on Algorithms, ESA 2024
Country/TerritoryUnited Kingdom
CityLondon
Period2/09/244/09/24

Keywords

  • Fine Grained Complexity
  • Kings
  • Query Complexity
  • Tournament Graphs

All Science Journal Classification (ASJC) codes

  • Software

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