eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-18
28:1
28:17
10.4230/LIPIcs.ESA.2016.28
article
Optimal Reachability and a Space-Time Tradeoff for Distance Queries in Constant-Treewidth Graphs
Chatterjee, Krishnendu
Rasmus Ibsen-Jensen, Rasmus
Pavlogiannis, Andreas
We consider data-structures for answering reachability and distance queries on constant-treewidth graphs with n nodes, on the standard RAM computational model with wordsize W=Theta(log n). Our first contribution is a data-structure that after O(n) preprocessing time, allows (1) pair reachability queries in O(1) time; and (2) single-source reachability queries in O(n/log n) time. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries. The data-structure uses at all times O(n) space. Our second contribution is a space-time tradeoff data-structure for distance queries. For any epsilon in [1/2,1], we provide a data-structure with polynomial preprocessing time that allows pair queries in O(n^{1-\epsilon} alpha(n)) time, where alpha is the inverse of the Ackermann function, and at all times uses O(n^epsilon) space. The input graph G is not considered in the space complexity.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol057-esa2016/LIPIcs.ESA.2016.28/LIPIcs.ESA.2016.28.pdf
Graph algorithms
Constant-treewidth graphs
Reachability queries
Distance queries