3 Search Results for "Bacic, Joyce"

Document
DOI: 10.4230/OASIcs.ATMOS.2024.2
Indexing Graphs for Shortest Beer Path Queries

Authors: David Coudert, Andrea D'Ascenzo, and Mattia D'Emidio

Published in: OASIcs, Volume 123, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)

Abstract
A beer graph is an edge-weighted graph G = (V,E,ω) with beer vertices B ⊆ V. A beer path between two vertices s and t of a beer graph is a path that connects s and t and visits at least one vertex in B. The beer distance between two vertices is the weight of a shortest beer path, i.e. a beer path having minimum total weight. A graph indexing scheme is a two-phase method that constructs an index data structure by a one-time preprocessing of an input graph and then exploits it to compute (or accelerate the computation of) answers to queries on structures of the graph dataset. In the last decade, such indexing schemes have been designed to perform, effectively, many relevant types of queries, e.g. on reachability, and have gained significant popularity in essentially all data-intensive application domains where large number of queries have to be routinely answered (e.g. journey planners), since they have been shown, through many experimental studies, to offer extremely low query times at the price of limited preprocessing time and space overheads. In this paper, we showcase that an indexing scheme, to efficiently execute queries on beer distances or shortest beer paths for pairs of vertices of a beer graph, can be obtained by adapting the highway labeling, a recently introduced indexing method to accelerate the computation of classical shortest paths. We design a preprocessing algorithm to build a whl index, i.e. a weighted highway labeling of a beer graph, and show how it can be queried to compute beer distances and shortest beer paths. Through extensive experimentation on real networks, we empirically demonstrate its practical effectiveness and superiority, in terms of offered trade-off between preprocessing time, space overhead and query time, with respect to the state-of-the-art.
Cite as

David Coudert, Andrea D'Ascenzo, and Mattia D'Emidio. Indexing Graphs for Shortest Beer Path Queries. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{coudert_et_al:OASIcs.ATMOS.2024.2,
  author =	{Coudert, David and D'Ascenzo, Andrea and D'Emidio, Mattia},
  title =	{{Indexing Graphs for Shortest Beer Path Queries}},
  booktitle =	{24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
  pages =	{2:1--2:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-350-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{123},
  editor =	{Bouman, Paul C. and Kontogiannis, Spyros C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.2},
  URN =		{urn:nbn:de:0030-drops-211907},
  doi =		{10.4230/OASIcs.ATMOS.2024.2},
  annote =	{Keywords: Graph Algorithms, Indexing Schemes, Beer Distances, Algorithms Engineering}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.25
Graph Spanners for Group Steiner Distances

Authors: Davide Bilò, Luciano Gualà, Stefano Leucci, and Alessandro Straziota

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
A spanner is a sparse subgraph of a given graph G which preserves distances, measured w.r.t. some distance metric, up to a multiplicative stretch factor. This paper addresses the problem of constructing graph spanners w.r.t. the group Steiner metric, which generalizes the recently introduced beer distance metric. In such a metric we are given a collection of groups of required vertices, and we measure the distance between two vertices as the length of the shortest path between them that traverses at least one required vertex from each group. We discuss the relation between group Steiner spanners and classic spanners and we show that they exhibit strong ties with sourcewise spanners w.r.t. the shortest path metric. Nevertheless, group Steiner spanners capture several interesting scenarios that are not encompassed by existing spanners. This happens, e.g., for the singleton case, in which each group consists of a single required vertex, thus modeling the setting in which routes need to traverse certain points of interests (in any order). We provide several constructions of group Steiner spanners for both the all-pairs and single-source case, which exhibit various size-stretch trade-offs. Notably, we provide spanners with almost-optimal trade-offs for the singleton case. Moreover, some of our spanners also yield novel trade-offs for classical sourcewise spanners. Finally, we also investigate the query times that can be achieved when our spanners are turned into group Steiner distance oracles with the same size, stretch, and building time.
Cite as

Davide Bilò, Luciano Gualà, Stefano Leucci, and Alessandro Straziota. Graph Spanners for Group Steiner Distances. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bilo_et_al:LIPIcs.ESA.2024.25,
  author =	{Bil\`{o}, Davide and Gual\`{a}, Luciano and Leucci, Stefano and Straziota, Alessandro},
  title =	{{Graph Spanners for Group Steiner Distances}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.25},
  URN =		{urn:nbn:de:0030-drops-210968},
  doi =		{10.4230/LIPIcs.ESA.2024.25},
  annote =	{Keywords: Network sparsification, Graph spanners, Group Steiner tree, Distance oracles}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.62
Shortest Beer Path Queries in Outerplanar Graphs

Authors: Joyce Bacic, Saeed Mehrabi, and Michiel Smid

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
A beer graph is an undirected graph G, in which each edge has a positive weight and some vertices have a beer store. A beer path between two vertices u and v in G is any path in G between u and v that visits at least one beer store. We show that any outerplanar beer graph G with n vertices can be preprocessed in O(n) time into a data structure of size O(n), such that for any two query vertices u and v, (i) the weight of the shortest beer path between u and v can be reported in O(α(n)) time (where α(n) is the inverse Ackermann function), and (ii) the shortest beer path between u and v can be reported in O(L) time, where L is the number of vertices on this path. Both results are optimal, even when G is a beer tree (i.e., a beer graph whose underlying graph is a tree).
Cite as

Joyce Bacic, Saeed Mehrabi, and Michiel Smid. Shortest Beer Path Queries in Outerplanar Graphs. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 62:1-62:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bacic_et_al:LIPIcs.ISAAC.2021.62,
  author =	{Bacic, Joyce and Mehrabi, Saeed and Smid, Michiel},
  title =	{{Shortest Beer Path Queries in Outerplanar Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{62:1--62:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.62},
  URN =		{urn:nbn:de:0030-drops-154950},
  doi =		{10.4230/LIPIcs.ISAAC.2021.62},
  annote =	{Keywords: shortest paths, outerplanar graph}
}
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