Spanner Approximations in Practice

TL;DR

This paper evaluates various algorithms for constructing multiplicative spanners in graphs, comparing their performance on multiple metrics through extensive experiments.

Contribution

It provides the first comprehensive experimental comparison of different spanner algorithms across multiple practical criteria.

Findings

Algorithms vary significantly in running time and sparseness.

Some algorithms produce lighter and more efficient spanners.

Performance depends on graph instances and desired properties.

Abstract

A multiplicative $\alpha$-spanner $H$ is a subgraph of $G=(V,E)$ with the same vertices and fewer edges that preserves distances up to the factor $\alpha$, i.e., $d_H(u,v)\leq\alpha\cdot d_G(u,v)$ for all vertices $u$, $v$. While many algorithms have been developed to find good spanners in terms of approximation guarantees, no experimental studies comparing different approaches exist. We implemented a rich selection of those algorithms and evaluate them on a variety of instances regarding, e.g., their running time, sparseness, lightness, and effective stretch.