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Titel:

Space-efficient algorithms for reachability in directed geometric graphs

AutorInnen:

Sujoy Bhore
Rahul Jain

Kategorie:

Artikel in Zeitschriften

erschienen in:

Theoretical Computer Science, Vol. 961, pp. 113938, 2023

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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Theoretical Computer Science

BibTeX-Eintrag:

@article{BHORE2023113938, title = {Space-efficient algorithms for reachability in directed geometric graphs}, journal = {Theoretical Computer Science}, volume = {961}, pages = {113938}, year = {2023}, issn = {0304-3975}, doi = {https://doi.org/10.1016/j.tcs.2023.113938}, url = {https://www.sciencedirect.com/science/article/pii/S0304397523002517}, author = {Sujoy Bhore and Rahul Jain}, }