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

Authors Rahul Jain , Raghunath Tewari

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Author Details

Rahul Jain
  • Indian Institute of Technology Kanpur, India
Raghunath Tewari
  • Indian Institute of Technology Kanpur, India

Funding

  • Jain, Rahul: Ministry of Human Resource Development, Government of India
  • Tewari, Raghunath: DST Inspire Faculty Grant, Visvesvaraya Young Faculty Fellowship

Acknowledgements

We thank anonymous reviewers for their helpful comments on an earlier version of this paper.

Cite AsGet BibTex

Rahul Jain and Raghunath Tewari. An O(n^(1/4 +epsilon)) Space and Polynomial Algorithm for Grid Graph Reachability. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.FSTTCS.2019.19

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • graph reachability
  • grid graph
  • graph algorithm
  • sublinear space algorithm

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