Improved algorithms for reachability and shortest path on low tree-width graphs

K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs, IST Austria, 2014.

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Technical Report | Published | English
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IST Austria Technical Report
Abstract
We consider the reachability and shortest path problems on low tree-width graphs, with n nodes, m edges, and tree-width t, on a standard RAM with wordsize W. We use O to hide polynomial factors of the inverse of the Ackermann function. Our main contributions are three fold: 1. For reachability, we present an algorithm that requires O(n·t2·log(n/t)) preprocessing time, O(n·(t·log(n/t))/W) space, and O(t/W) time for pair queries and O((n·t)/W) time for single-source queries. Note that for constant t our algorithm uses O(n·logn) time for preprocessing; and O(n/W) time for single-source queries, which is faster than depth first search/breath first search (after the preprocessing). 2. We present an algorithm for shortest path that requires O(n·t2) preprocessing time, O(n·t) space, and O(t2) time for pair queries and O(n·t) time single-source queries. 3. We give a space versus query time trade-off algorithm for shortest path that, given any constant >0, requires O(n·t2) preprocessing time, O(n·t2) space, and O(n1−·t2) time for pair queries. Our algorithms improve all existing results, and use very simple data structures.
Publishing Year
Date Published
2014-04-14
Page
34
ISSN
IST-REx-ID

Cite this

Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs. IST Austria; 2014. doi:10.15479/AT:IST-2014-187-v1-1
Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2014). Improved algorithms for reachability and shortest path on low tree-width graphs. IST Austria. https://doi.org/10.15479/AT:IST-2014-187-v1-1
Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-187-v1-1.
K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, Improved algorithms for reachability and shortest path on low tree-width graphs. IST Austria, 2014.
Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2014. Improved algorithms for reachability and shortest path on low tree-width graphs, IST Austria, 34p.
Chatterjee, Krishnendu, et al. Improved Algorithms for Reachability and Shortest Path on Low Tree-Width Graphs. IST Austria, 2014, doi:10.15479/AT:IST-2014-187-v1-1.
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