eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-11-28
12:1
12:14
10.4230/LIPIcs.ISAAC.2019.12
article
Reachability in High Treewidth Graphs
Jain, Rahul
1
https://orcid.org/0000-0002-8567-9475
Tewari, Raghunath
1
Indian Institute of Technology Kanpur, India
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol149-isaac2019/LIPIcs.ISAAC.2019.12/LIPIcs.ISAAC.2019.12.pdf
graph reachability
simultaneous time-space upper bound
tree decomposition