DeepAI AI Chat
Log In Sign Up

Communication Complexity of Collision

07/29/2022
by   Mika Göös, et al.
0

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).

READ FULL TEXT

page 1

page 2

page 3

page 4

01/04/2019

A New Approach to Multi-Party Peer-to-Peer Communication Complexity

We introduce new models and new information theoretic measures for the s...
08/14/2022

An improved lower bound on the length of the longest cycle in random graphs

We provide a new lower bound on the length of the longest cycle of the b...
07/03/2018

Detecting cliques in CONGEST networks

The problem of detecting network structures plays a central role in dist...
12/29/2017

Quantum Lower Bound for a Tripartite Version of the Hidden Shift Problem

In this paper, we prove a polynomial lower bound of Ω(n^1/3) on the quan...
07/23/2018

SETH Says: Weak Fréchet Distance is Faster, but only if it is Continuous and in One Dimension

We show by reduction from the Orthogonal Vectors problem that algorithms...
05/24/2021

A Simple Proof of a New Set Disjointness with Applications to Data Streams

The multiplayer promise set disjointness is one of the most widely used ...
06/13/2019

The Communication Complexity of Optimization

We consider the communication complexity of a number of distributed opti...