2026-07-26T11:14:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11884 2024-03-06T10:48:55Z ddc:004 open_access

Quantum Distributed Algorithm for Triangle Finding in the CONGEST Model Izumi, Taisuke Le Gall, François Magniez, Frédéric Quantum computing distributed computing CONGEST model This paper considers the triangle finding problem in the CONGEST model of distributed computing. Recent works by Izumi and Le Gall (PODC'17), Chang, Pettie and Zhang (SODA'19) and Chang and Saranurak (PODC'19) have successively reduced the classical round complexity of triangle finding (as well as triangle listing) from the trivial upper bound O(n) to Õ(n^{1/3}), where n denotes the number of vertices in the graph. In this paper we present a quantum distributed algorithm that solves the triangle finding problem in Õ(n^{1/4}) rounds in the CONGEST model. This gives another example of quantum algorithm beating the best known classical algorithms in distributed computing. Our result also exhibits an interesting phenomenon: while in the classical setting the best known upper bounds for the triangle finding and listing problems are identical, in the quantum setting the round complexities of these two problems are now Õ(n^{1/4}) and Θ~(n^{1/3}), respectively. Our result thus shows that triangle finding is easier than triangle listing in the quantum CONGEST model. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Taisuke Izumi and François Le Gall and Frédéric Magniez 2020 Is Part Of LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2020.23 urn:nbn:de:0030-drops-118840 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.23 eng https://creativecommons.org/licenses/by/3.0/legalcode