License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2019.19
URN: urn:nbn:de:0030-drops-115813
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11581/
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Jain, Rahul ; Tewari, Raghunath

An O(n^(1/4 +epsilon)) Space and Polynomial Algorithm for Grid Graph Reachability

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LIPIcs-FSTTCS-2019-19.pdf (0.6 MB)

Abstract

The reachability problem is to determine if there exists a path from one vertex to another in a graph. Grid graphs are the class of graphs where vertices are present on the lattice points of a two-dimensional grid, and an edge can occur between a vertex and its immediate horizontal or vertical neighbor only.
Asano et al. presented the first simultaneous time space bound for reachability in grid graphs by presenting an algorithm that solves the problem in polynomial time and O(n^(1/2 + epsilon)) space. In 2018, the space bound was improved to O~(n^(1/3)) by Ashida and Nakagawa.
In this paper, we show that reachability in an n vertex grid graph can be decided by an algorithm using O(n^(1/4 + epsilon)) space and polynomial time simultaneously.

BibTeX - Entry

@InProceedings{jain_et_al:LIPIcs:2019:11581,
  author =	{Rahul Jain and Raghunath Tewari},
  title =	{{An O(n^(1/4 +epsilon)) Space and Polynomial Algorithm for Grid Graph Reachability}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Arkadev Chattopadhyay and Paul Gastin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11581},
  URN =		{urn:nbn:de:0030-drops-115813},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.19},
  annote =	{Keywords: graph reachability, grid graph, graph algorithm, sublinear space algorithm}
}

Keywords: graph reachability, grid graph, graph algorithm, sublinear space algorithm
Collection: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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