Eccentricity queries and beyond using Hub Labels
Guillaume Ducoffe

TL;DR
This paper explores the use of hub labeling schemes for efficient computation of eccentricity and distance-sum queries on large graphs, revealing both limitations and new efficient algorithms for special cases.
Contribution
It introduces algorithms for fast eccentricity and distance-sum queries using small hub labels, and establishes lower bounds for these problems on certain graph classes.
Findings
Conditional lower bounds for unweighted undirected sparse graphs.
Efficient algorithms for graphs with sublogarithmic hub labels.
Fast diameter decision in bounded expansion graph classes.
Abstract
Hub labeling schemes are popular methods for computing distances on road networks and other large complex networks, often answering to a query within a few microseconds for graphs with millions of edges. In this work, we study their algorithmic applications beyond distance queries. We focus on eccentricity queries and distance-sum queries, for several versions of these problems on directed weighted graphs, that is in part motivated by their importance in facility location problems. On the negative side, we show conditional lower bounds for these above problems on unweighted undirected sparse graphs, via standard constructions from "Fine-grained" complexity. However, things take a different turn when the hub labels have a sublogarithmic size. Indeed, given a hub labeling of maximum label size , after pre-processing the labels in total time, we can…
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Taxonomy
TopicsDigital Image Processing Techniques · Graph Labeling and Dimension Problems · Advanced Graph Theory Research
