English

The communication complexity of the inevitable intersection problem

Computational Complexity 2022-03-30 v3

Abstract

Set disjointness is a central problem in communication complexity. Here Alice and Bob each receive a subset of an n-element universe, and they need to decide whether their inputs intersect or not. The communication complexity of this problem is relatively well understood, and in most models, including - most famously - interactive randomised communication with bounded error, the problem requires much communication. In this work we were looking for a variation of the set disjointness problem, as natural and simple as possible, for which the known lower bound methods would fail, and thus a new approach would be required in order to understand its complexity. The problem that we have found is a relational one: each player receives a subset as input, and the goal is to find an element that belongs to both players. We call it inevitable intersection.

Keywords

Cite

@article{arxiv.1611.08842,
  title  = {The communication complexity of the inevitable intersection problem},
  author = {Dmytro Gavinsky},
  journal= {arXiv preprint arXiv:1611.08842},
  year   = {2022}
}
R2 v1 2026-06-22T17:05:24.550Z