Space-Efficient Path-Reporting Approximate Distance Oracles

TL;DR

This paper introduces space-efficient approximate path-reporting distance oracles, labeling, and routing schemes for undirected graphs, improving space bounds at the cost of increased stretch.

Contribution

It presents methods to reduce space requirements for path-reporting oracles and labeling schemes beyond previous bounds, with a trade-off in stretch.

Findings

Breaks the n log n space bound for path-reporting oracles

Reduces space per vertex below O(log n) words for labeling and routing

Achieves these with increased stretch in approximation

Abstract

We consider approximate {\em path-reporting} distance oracles, distance labeling and labeled routing with extremely low space requirement, for general undirected graphs. For distance oracles, we show how to break the n\log n space bound of Thorup and Zwick if approximate {\em paths} rather than distances need to be reported. For approximate distance labeling and labeled routing, we break the previously best known space bound of O(log n) words per vertex. The cost for such space efficiency is an increased stretch.