Communication Complexity of Collision

Authors Mika Göös, Siddhartha Jain

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Author Details

Mika Göös
  • EPFL, Lausanne, Switzerland
Siddhartha Jain
  • EPFL, Lausanne, Switzerland


We thank anonymous RANDOM reviewers for their helpful comments.

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Mika Göös and Siddhartha Jain. Communication Complexity of Collision. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 19:1-19:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Collision
  • Communication complexity
  • Lifting


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