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DOI: 10.4230/LIPIcs.ICALP.2017.124
URN: urn:nbn:de:0030-drops-74398
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7439/
Bringmann, Karl ; Dueholm Hansen, Thomas ; Krinninger, Sebastian
Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs
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Abstract
We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with n nodes and m edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in the context of quantitative verification. We focus on strongly polynomial algorithms to cover the use-case where the weights are relatively large compared to the size of the graph. Our main result is an algorithm with running time ~O(m^{3/4} n^{3/2}), which gives the first improvement over Megiddo's ~O(n^3) algorithm [JACM'83] for sparse graphs (We use the notation ~O(.) to hide factors that are polylogarithmic in n.) We further demonstrate how to obtain both an algorithm with running time n^3/2^{Omega(sqrt(log n)} on general graphs and an algorithm with running time ~O(n) on constant treewidth graphs. To obtain our main result, we develop a parallel algorithm for negative cycle detection and single-source shortest paths that might be of independent interest.
BibTeX - Entry
@InProceedings{bringmann_et_al:LIPIcs:2017:7439,
author = {Karl Bringmann and Thomas Dueholm Hansen and Sebastian Krinninger},
title = {{Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs}},
booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages = {124:1--124:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-041-5},
ISSN = {1868-8969},
year = {2017},
volume = {80},
editor = {Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7439},
URN = {urn:nbn:de:0030-drops-74398},
doi = {10.4230/LIPIcs.ICALP.2017.124},
annote = {Keywords: quantitative verification and synthesis, parametric search, shortest paths, negative cycle detection}
}
| Keywords: | quantitative verification and synthesis, parametric search, shortest paths, negative cycle detection | |
| Seminar: | 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 07.07.2017 |
