TY - GEN

T1 - Exploiting hopsets

T2 - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

AU - Gupta, Siddharth

AU - Kosowski, Adrian

AU - Viennot, Laurent

N1 - Funding Information:
Siddharth Gupta: Supported in part by the Zuckerman STEM Leadership Program. Adrian Kosowski: Supported by ANR project DESCARTES (ANR-16-CE40-0023).
Publisher Copyright:
© Siddharth Gupta, Adrian Kosowski, and Laurent Viennot; licensed under Creative Commons License CC-BY

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - Data Structures

KW - Distance Oracles

KW - Graph Algorithms

KW - Hopsets

UR - http://www.scopus.com/inward/record.url?scp=85069198401&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2019.143

DO - 10.4230/LIPIcs.ICALP.2019.143

M3 - Conference contribution

AN - SCOPUS:85069198401

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

A2 - Baier, Christel

A2 - Chatzigiannakis, Ioannis

A2 - Flocchini, Paola

A2 - Leonardi, Stefano

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Y2 - 9 July 2019 through 12 July 2019

ER -