Random Rank-Based, Hierarchical or Trivial: Which Dynamic Graph Algorithm Performs Best in Practice?

TL;DR

This paper compares the practical performance of hierarchical and random-rank based dynamic graph algorithms for coloring and matching, revealing that data structure choice significantly impacts efficiency.

Contribution

It provides an extensive experimental evaluation of two types of dynamic graph algorithms and simple baselines for coloring and matching problems.

Findings

Data structure choice dominates algorithm performance

Hierarchical and random-rank algorithms perform variably depending on the problem

Simple baseline algorithms are competitive in practice

Abstract

Fully dynamic graph algorithms that achieve polylogarithmic or better time per operation use either a hierarchical graph decomposition or random-rank based approach. There are so far two graph properties for which efficient algorithms for both types of data structures exist, namely fully dynamic (Delta + 1) coloring and fully dynamic maximal matching. In this paper we present an extensive experimental study of these two types of algorithms for these two problems together with very simple baseline algorithms to determine which of these algorithms are the fastest. Our results indicate that the data structures used by the different algorithms dominate their performance.