Reachability in High Treewidth Graphs
Rahul Jain
Raghunath Tewari
erschienen in:
30th International Symposium on Algorithms and Computation (ISAAC 2019), LIPIcs, Vol. 149, pp. 12:1-12:14

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.

@InProceedings{jain_et_al:LIPIcs:2019:11508, author = {Rahul Jain and Raghunath Tewari}, title = {{Reachability in High Treewidth Graphs}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {12:1--12:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Pinyan Lu and Guochuan Zhang}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, URL = {}, URN = {urn:nbn:de:0030-drops-115087}, doi = {10.4230/LIPIcs.ISAAC.2019.12}, annote = {Keywords: graph reachability, simultaneous time-space upper bound, tree decomposition} }
Christoph Doppelbauer | 10.05.2024