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Computer Science > Computational Complexity
[Submitted on 27 Nov 2016 (v1), last revised 31 Aug 2020 (this version, v3)]
The communication complexity of the inevitable intersection problem
Dmitry Gavinsky
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.
Subjects:
Computational Complexity (cs.CC)
Cite as:
arXiv:1611.08842 [cs.CC]
(or arXiv:1611.08842v3 [cs.CC] for this version)
Submission history
From: Dmitry Gavinsky [view email]
[v1] Sun, 27 Nov 2016 13:47:16 UTC (15 KB)
[v2] Sun, 21 May 2017 00:54:02 UTC (13 KB)
[v3] Mon, 31 Aug 2020 01:28:48 UTC (17 KB)
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