2026-07-21T14:19:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15496 2024-03-06T10:55:26Z ddc:004 open_access

Space-Efficient Algorithms for Reachability in Directed Geometric Graphs Bhore, Sujoy Jain, Rahul Reachablity Geometric intersection graphs Space-efficient algorithms 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sujoy Bhore and Rahul Jain 2021 Is Part Of LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2021.63 urn:nbn:de:0030-drops-154961 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.63 eng https://creativecommons.org/licenses/by/4.0/legalcode