# Greedy maximal independent sets via local limits

## TL;DR

This paper introduces a general framework using local limits to analyze the asymptotic density of random greedy maximal independent sets across various graph families, simplifying proofs and extending results.

## Contribution

It develops a unified approach for analyzing the random greedy algorithm on diverse graph sequences via local convergence, including new results on trees and planar graphs.

## Key findings

- Framework applies to paths, random graphs, trees, and planar graphs.
- Simplifies proofs of known results.
- Provides new insights into the algorithm on trees.

## 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.