@inproceedings{2b9a4f613b31478ca75287595e0f3b56,
title = "From Donkeys to Kings in Tournaments",
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.",
keywords = "Fine Grained Complexity, Kings, Query Complexity, Tournament Graphs",
author = "Amir Abboud and Tomer Grossman and Moni Naor and Tomer Solomon",
note = "Publisher Copyright: {\textcopyright} Amir Abboud, Tomer Grossman, Moni Naor, and Tomer Solomon; licensed under Creative Commons License CC-BY 4.0.; 32nd Annual European Symposium on Algorithms, ESA 2024 ; Conference date: 02-09-2024 Through 04-09-2024",
year = "2024",
month = sep,
day = "23",
doi = "https://doi.org/10.4230/LIPIcs.ESA.2024.3",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Timothy Chan and Johannes Fischer and John Iacono and Grzegorz Herman",
booktitle = "32nd Annual European Symposium on Algorithms, ESA 2024",
address = "ألمانيا",
}