Veröffentlichung

Titel:

Space-Efficient Algorithms for Reachability in Directed Geometric Graphs

AutorInnen:

Sujoy Bhore
Rahul Jain

Kategorie:

Konferenzbandbeiträge

erschienen in:

Leibniz International Proceedings in Informatics (LIPIcs) - 32nd International Symposium on Algorithms and Computation (ISAAC 2021), Vol. 212, pp. 63:1-63:17, 2021

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.

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BibTeX-Eintrag:

@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} }