License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2021.63
URN: urn:nbn:de:0030-drops-154961
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15496/
Bhore, Sujoy ;
Jain, Rahul
Space-Efficient Algorithms for Reachability in Directed Geometric Graphs
Abstract
The problem of graph Reachability is to decide whether there is a path from one vertex to another in a given graph. In this paper, we study the Reachability problem on three distinct graph families - intersection graphs of Jordan regions, unit contact disk graphs (penny graphs), and chordal graphs. For each of these graph families, we present space-efficient algorithms for the Reachability problem.
For intersection graphs of Jordan regions, we show how to obtain a "good" vertex separator in a space-efficient manner and use it to solve the Reachability in polynomial time and O(m^{1/2} log n) space, where n is the number of Jordan regions, and m is the total number of crossings among the regions. We use a similar approach for chordal graphs and obtain a polynomial time and O(m^{1/2} log n) space algorithm, where n and m are the number of vertices and edges, respectively. However, for unit contact disk graphs (penny graphs), we use a more involved technique and obtain a better algorithm. We show that for every ε > 0, there exists a polynomial time algorithm that can solve Reachability in an n vertex directed penny graph, using O(n^{1/4+ε}) space. We note that the method used to solve penny graphs does not extend naturally to the class of geometric intersection graphs that include arbitrary size cliques.
BibTeX - Entry
@InProceedings{bhore_et_al:LIPIcs.ISAAC.2021.63,
author = {Bhore, Sujoy and Jain, Rahul},
title = {{Space-Efficient Algorithms for Reachability in Directed Geometric Graphs}},
booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
pages = {63:1--63:17},
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/opus/volltexte/2021/15496},
URN = {urn:nbn:de:0030-drops-154961},
doi = {10.4230/LIPIcs.ISAAC.2021.63},
annote = {Keywords: Reachablity, Geometric intersection graphs, Space-efficient algorithms}
}
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Keywords: |
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Reachablity, Geometric intersection graphs, Space-efficient algorithms |
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Collection: |
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32nd International Symposium on Algorithms and Computation (ISAAC 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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30.11.2021 |
