The communication complexity of the inevitable intersection problem
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}
}