Optimal reachability and a space time tradeoff for distance queries in constant treewidth graphs

K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016.

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Conference Paper | Published | English
Department
Series Title
LIPIcs
Abstract
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.
Publishing Year
Date Published
2016-08-01
Acknowledgement
The research was partly supported by Austrian Science Fund (FWF) Grant No P23499-N23, FWF NFN Grant No S11407-N23 (RiSE/SHiNE) and ERC Start grant (279307: Graph Games).
Volume
57
Article Number
28
Conference
ESA: European Symposium on Algorithms
Conference Location
Aarhus, Denmark
Conference Date
2016-08-22 – 2016-08-24
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Cite this

Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Optimal reachability and a space time tradeoff for distance queries in constant treewidth graphs. In: Vol 57. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik; 2016. doi:10.4230/LIPIcs.ESA.2016.28
Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2016). Optimal reachability and a space time tradeoff for distance queries in constant treewidth graphs (Vol. 57). Presented at the ESA: European Symposium on Algorithms, Aarhus, Denmark: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik. https://doi.org/10.4230/LIPIcs.ESA.2016.28
Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. “Optimal Reachability and a Space Time Tradeoff for Distance Queries in Constant Treewidth Graphs,” Vol. 57. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016. https://doi.org/10.4230/LIPIcs.ESA.2016.28.
K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, “Optimal reachability and a space time tradeoff for distance queries in constant treewidth graphs,” presented at the ESA: European Symposium on Algorithms, Aarhus, Denmark, 2016, vol. 57.
Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2016. Optimal reachability and a space time tradeoff for distance queries in constant treewidth graphs. ESA: European Symposium on Algorithms, LIPIcs, vol. 57.
Chatterjee, Krishnendu, et al. Optimal Reachability and a Space Time Tradeoff for Distance Queries in Constant Treewidth Graphs. Vol. 57, 28, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016, doi:10.4230/LIPIcs.ESA.2016.28.
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