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Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond

Authors Siddharth Gupta, Adrian Kosowski, Laurent Viennot

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Author Details

Siddharth Gupta
  • Ben-Gurion University of the Negev, Israel
Adrian Kosowski
  • Inria, Paris, France
Laurent Viennot
  • Inria, Paris, France

Funding

  • Gupta, Siddharth: Supported in part by the Zuckerman STEM Leadership Program.
  • Kosowski, Adrian: Supported by ANR project DESCARTES (ANR-16-CE40-0023).
  • Viennot, Laurent: Supported by ANR project DISTANCIA (ANR-17-CE40-0015) and ANR project MULTIMOD (ANR-17-CE22-0016).

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Siddharth Gupta, Adrian Kosowski, and Laurent Viennot. Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 143:1-143:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ICALP.2019.143

Abstract

For fixed h >= 2, we consider the task of adding to a graph G a set of weighted shortcut edges on the same vertex set, such that the length of a shortest h-hop path between any pair of vertices in the augmented graph is exactly the same as the original distance between these vertices in G. A set of shortcut edges with this property is called an exact h-hopset and may be applied in processing distance queries on graph G. In particular, a 2-hopset directly corresponds to a distributed distance oracle known as a hub labeling. In this work, we explore centralized distance oracles based on 3-hopsets and display their advantages in several practical scenarios. In particular, for graphs of constant highway dimension, and more generally for graphs of constant skeleton dimension, we show that 3-hopsets require exponentially fewer shortcuts per node than any previously described distance oracle, and also offer a speedup in query time when compared to simple oracles based on a direct application of 2-hopsets. Finally, we consider the problem of computing minimum-size h-hopset (for any h >= 2) for a given graph G, showing a polylogarithmic-factor approximation for the case of unique shortest path graphs. When h=3, for a given bound on the space used by the distance oracle, we provide a construction of hopset achieving polylog approximation both for space and query time compared to the optimal 3-hopset oracle given the space bound.

Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Data structures design and analysis
Keywords
  • Hopsets
  • Distance Oracles
  • Graph Algorithms
  • Data Structures

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