Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.10
URN: urn:nbn:de:0030-drops-57116
URL: https://drops.dagstuhl.de/opus/volltexte/2016/5711/
Arora, Rahul ; Gupta, Ashu ; Gurjar, Rohit ; Tewari, Raghunath
Derandomizing Isolation Lemma for K3,3-free and K5-free Bipartite Graphs
| pdf-format: |
|
Abstract
The perfect matching problem has a randomized NC algorithm, using the celebrated Isolation Lemma of Mulmuley, Vazirani and Vazirani. The Isolation Lemma states that giving a random weight assignment to the edges of a graph ensures that it has a unique minimum weight perfect matching, with a good probability. We derandomize this lemma for K3,3-free and K5-free bipartite graphs. That is, we give a deterministic log-space construction of such a weight assignment for these graphs. Such a construction was known previously for planar bipartite graphs. Our result implies that the perfect matching problem for K3,3-free and K5-free bipartite graphs is in SPL. It also gives an alternate proof for an already known result – reachability for K3,3-free and K5-free graphs is in UL.
BibTeX - Entry
@InProceedings{arora_et_al:LIPIcs:2016:5711,
author = {Rahul Arora and Ashu Gupta and Rohit Gurjar and Raghunath Tewari},
title = {{Derandomizing Isolation Lemma for K3,3-free and K5-free Bipartite Graphs}},
booktitle = {33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
pages = {10:1--10:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-001-9},
ISSN = {1868-8969},
year = {2016},
volume = {47},
editor = {Nicolas Ollinger and Heribert Vollmer},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5711},
URN = {urn:nbn:de:0030-drops-57116},
doi = {10.4230/LIPIcs.STACS.2016.10},
annote = {Keywords: bipartite matching, derandomization, isolation lemma, SPL, minor-free graph}
}
| Keywords: | bipartite matching, derandomization, isolation lemma, SPL, minor-free graph | |
| Seminar: | 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 16.02.2016 |
