## 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}logn) 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}logn) 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.

Original language | English |
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Article number | 113938 |

Journal | Theoretical Computer Science |

Volume | 961 |

DOIs | |

State | Published - 15 Jun 2023 |

Externally published | Yes |

## Keywords

- Geometric intersection graphs
- Reachability
- Space-efficient algorithms

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science