2026-07-22T10:47:12Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17141 2024-03-06T10:59:04Z ddc:004 open_access

Communication Complexity of Collision Göös, Mika Jain, Siddhartha Collision Communication complexity Lifting The Collision problem is to decide whether a given list of numbers (x_1,…,x_n) ∈ [n]ⁿ is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n^Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x_i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov (CCC 2021). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mika Göös and Siddhartha Jain 2022 Is Part Of LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2022.19 urn:nbn:de:0030-drops-171415 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.19 eng https://creativecommons.org/licenses/by/4.0/legalcode