An Experimental Study of the Treewidth of Real-World Graph Data (Extended Version)

TL;DR

This study empirically investigates the treewidth of real-world graph datasets to understand their decomposability and potential for efficient algorithmic processing, revealing that partial decompositions can be beneficial even for high treewidth data.

Contribution

First large-scale experimental analysis of treewidth in real-world databases, providing bounds and insights into their decompositions and algorithmic utility.

Findings

High treewidth datasets often benefit from partial decompositions

Treewidth bounds vary significantly across datasets

Partial tree decompositions can aid algorithms despite high overall treewidth

Abstract

Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the treewidth of a given instance is intractable. This article is the first large-scale experimental study of treewidth and tree decompositions of real-world database instances (25 datasets from 8 different domains, with sizes ranging from a few thousand to a few million vertices). The goal is to determine which data, if any, can benefit of the wealth of algorithms for databases of small treewidth. For each dataset, we obtain upper and lower bound estimations of their treewidth, and study the properties of their tree decompositions. We show in particular that, even when treewidth is high, using partial tree decompositions can result in data structures that can assist algorithms.