A Breezing Proof of the KMW Bound

02/14/2020
by   Corinna Coupette, et al.
0

In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with n nodes and maximum degree Δ on which Ω(min{√(log n/loglog n),logΔ/loglogΔ}) (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching, respectively. Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings. Today, more than 15 years later, there is still no proof of this result that is easy on the reader. Setting out to change this, in this work, we provide a fully self-contained and simple proof of the KMW lower bound. The key argument is algorithmic, and it relies on an invariant that can be readily verified from the generation rules of the lower bound graphs.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/27/2019

Improved Distributed Approximation to Maximum Independent Set

We present improved results for approximating Maximum Independent Set ()...
research
11/03/2022

Distributed Maximal Matching and Maximal Independent Set on Hypergraphs

We investigate the distributed complexity of maximal matching and maxima...
research
04/17/2020

Distributed Lower Bounds for Ruling Sets

Given a graph G = (V,E), an (α, β)-ruling set is a subset S ⊆ V such tha...
research
06/04/2021

Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in Trees

Recently, Balliu, Brandt, and Olivetti [FOCS '20] showed the first ω(log...
research
05/24/2019

Hardness of Distributed Optimization

This paper studies lower bounds for fundamental optimization problems in...
research
08/20/2020

A Simple Proof of Optimal Approximations

The fundamental result of Li, Long, and Srinivasan on approximations of ...
research
06/13/2020

When Algorithms for Maximal Independent Set and Maximal Matching Run in Sublinear-Time

Maximal independent set (MIS), maximal matching (MM), and (Δ+1)-coloring...

Please sign up or login with your details

Forgot password? Click here to reset