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Reachability in High Treewidth Graphs

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

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Rahul Jain and Raghunath Tewari. Reachability in High Treewidth Graphs. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ISAAC.2019.12

Abstract

Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability; however, their space complexity is also linear. On the other hand, Savitch’s algorithm takes quasipolynomial time although the space bound is O(log^2 n). Here, we study space efficient algorithms for deciding reachability that run in polynomial time. 
In this paper, we show that given an n vertex directed graph of treewidth w along with its tree decomposition, there exists an algorithm running in polynomial time and O(w log n) space that solves the reachability problem.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • graph reachability
  • simultaneous time-space upper bound
  • tree decomposition

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