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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

Acknowledgements

We thank anonymous RANDOM reviewers for their helpful comments.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.19

Abstract

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
Keywords
  • Collision
  • Communication complexity
  • Lifting

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