Rainbow Greedy Matching Algorithms

TL;DR

This paper analyzes the effectiveness of two greedy algorithms designed to find large rainbow matchings in randomly edge-colored graphs, extending previous work on uncolored matchings.

Contribution

It introduces and evaluates two greedy algorithms specifically tailored for rainbow matchings in random graphs, building on existing algorithms for uncolored matchings.

Findings

Both algorithms perform effectively in finding large rainbow matchings.

The analysis provides insights into the algorithms' performance in random graph models.

Results suggest potential for improved algorithms in rainbow matching problems.

Abstract

We consider the problem of finding a large rainbow matching in a random graph with randomly colored edges. In particular we analyze the performance of two greedy algorithms for this problem. The algorithms we study are colored versions of algorithms that were previously used to find large matchings in random graphs (i.e. the color-free version of our present problem).