2026-07-18T09:09:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23398 2025-10-02T12:54:04Z ddc:004 open_access

Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles Beame, Paul Whitmeyer, Michael Proof Complexity Communication Complexity We prove several results concerning the communication complexity of a collision-finding problem, each of which has applications to the complexity of cutting-plane proofs, which make inferences based on integer linear inequalities. In particular, we prove an Ω(n^{1-1/k} log k /2^k) lower bound on the k-party number-in-hand communication complexity of collision-finding. This implies a 2^{n^{1-o(1)}} lower bound on the size of tree-like cutting-planes refutations of the bit pigeonhole principle CNFs, which are compact and natural propositional encodings of the negation of the pigeonhole principle, improving on the best previous lower bound of 2^{Ω(√n)}. Using the method of density-restoring partitions, we also extend that previous lower bound to the full range of pigeonhole parameters. Finally, using a refinement of a bottleneck-counting framework of Haken and Cook and Sokolov for DAG-like communication protocols, we give a 2^{Ω(n^{1/4})} lower bound on the size of fully general (not necessarily tree-like) cutting planes refutations of the same bit pigeonhole principle formulas, improving on the best previous lower bound of 2^{Ω(n^{1/8})}. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Paul Beame and Michael Whitmeyer 2025 Is Part Of LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2025.21 urn:nbn:de:0030-drops-233982 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.21 eng https://creativecommons.org/licenses/by/4.0/legalcode