Communication Complexity of Collision
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). LIPIcs, Vol. 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022), pages 19:1-19:9
2022
978-3-95977-249-5
245
19:1
19:9
REVIEWED
Event name | Event place | Event date |
University of Illinois, Urbana-Champaign, USA (Virtual Conference) | September 19-21, 2022 | |