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Séminaire Algo - Laurent Viennot
Séminaire Algo - Laurent Viennot
12-déc.-2017 14:30
Il y a: 68 days

Laurent Viennot

Beyond Highway Dimension: Small Distance Labels Using Tree Skeletons

Salle de séminaire (4B05R) - Bâtiment Copernic

Abstract: The goal of a hub-based distance labeling scheme for a network G = (V, E) is to assign a small subset S(u) ⊆ V to each node u ∈ V, in such a way that for any pair of nodes u, v, the intersection of hub sets S(u) ∩ S(v) contains a node on the shortest uv-path. The existence of small hub sets, and consequently efficient shortest path processing algorithms, for road networks is an empirical observation. A theoretical explanation for this phenomenon was proposed by Abraham et al. (SODA 2010) through a network parameter they called highway dimension, which captures the size of a hitting set for a collection of shortest paths of length at least r intersecting a given ball of radius 2r. In this work, we revisit this explanation, introducing a more tractable (and directly comparable) parameter based solely on the structure of shortest-path spanning trees, which we call skeleton dimension. We show that skeleton dimension admits an intuitive definition for both directed and undirected graphs, provides a way of computing labels more efficiently than by using highway dimension, and leads to comparable or stronger theoretical bounds on hub set size.

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