Eccentricity queries and beyond using Hub Labels
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by
Guillaume Ducoffe
2020
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 ≤ k, after
pre-processing the labels in total 2^O(k)· |V|^1+o(1) time, we can
compute both the eccentricity and the distance-sum of any vertex in 2^O(k)· |V|^o(1) time. It can also be applied to the fast global computation
of some topological indices. Finally, as a by-product of our approach, on any
fixed class of unweighted graphs with bounded expansion, we can decide whether
the diameter of an n-vertex graph in the class is at most k in f(k) ·
n^1+o(1) time, for some "explicit" function f.
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