Optimal tree-decomposition balancing and reachability on low treewidth graphs

K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs, IST Austria, 2014.

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Technical Report | Published | English
Department
Series Title
IST Austria Technical Report
Abstract
We consider graphs with n nodes together with their tree-decomposition that has b = O ( n ) bags and width t , on the standard RAM computational model with wordsize W = Θ (log n ) . Our contributions are two-fold: Our first contribution is an algorithm that given a graph and its tree-decomposition as input, computes a binary and balanced tree-decomposition of width at most 4 · t + 3 of the graph in O ( b ) time and space, improving a long-standing (from 1992) bound of O ( n · log n ) time for constant treewidth graphs. Our second contribution is on reachability queries for low treewidth graphs. We build on our tree-balancing algorithm and present a data-structure for graph reachability that requires O ( n · t 2 ) preprocessing time, O ( n · t ) space, and O ( d t/ log n e ) time for pair queries, and O ( n · t · log t/ log n ) time for single-source queries. For constant t our data-structure uses O ( n ) time for preprocessing, O (1) time for pair queries, and O ( n/ log n ) time for single-source queries. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries.
Publishing Year
Date Published
2014-11-05
Page
24
ISSN
IST-REx-ID

Cite this

Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs. IST Austria; 2014. doi:10.15479/AT:IST-2014-314-v1-1
Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2014). Optimal tree-decomposition balancing and reachability on low treewidth graphs. IST Austria. https://doi.org/10.15479/AT:IST-2014-314-v1-1
Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-314-v1-1.
K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, Optimal tree-decomposition balancing and reachability on low treewidth graphs. IST Austria, 2014.
Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2014. Optimal tree-decomposition balancing and reachability on low treewidth graphs, IST Austria, 24p.
Chatterjee, Krishnendu, et al. Optimal Tree-Decomposition Balancing and Reachability on Low Treewidth Graphs. IST Austria, 2014, doi:10.15479/AT:IST-2014-314-v1-1.
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