2026-08-17T12:13:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:10719 2024-03-06T10:46:33Z ddc:004 open_access

Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond Gupta, Siddharth Kosowski, Adrian Viennot, Laurent Hopsets Distance Oracles Graph Algorithms Data Structures 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Siddharth Gupta and Adrian Kosowski and Laurent Viennot 2019 Is Part Of LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2019.143 urn:nbn:de:0030-drops-107199 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.143 eng https://creativecommons.org/licenses/by/3.0/legalcode