Greedy maximal independent sets via local limits

Michael Krivelevich, Tamás Mészáros, Peleg Michaeli, Clara Shikhelman

Research output: Contribution to journalArticlepeer-review

Abstract

The random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent to any previously added vertex. In this paper, we present a general framework for computing the asymptotic density of the random greedy independent set for sequences of (possibly random) graphs by employing a notion of local convergence. We use this framework to give straightforward proofs for results on previously studied families of graphs, like paths and binomial random graphs, and to study new ones, like random trees and sparse random planar graphs. We conclude by analysing the random greedy algorithm more closely when the base graph is a tree.

Original languageEnglish
Pages (from-to)986-1015
Number of pages30
JournalRandom Structures and Algorithms
Volume64
Issue number4
DOIs
StateAccepted/In press - 2023

Keywords

  • greedy maximal independent set
  • local limit
  • random graph

All Science Journal Classification (ASJC) codes

  • Software
  • Applied Mathematics
  • General Mathematics
  • Computer Graphics and Computer-Aided Design

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