Kor, Liah ;
Korman, Amos ;
Peleg, David
Tight Bounds For Distributed MST Verification
Abstract
This paper establishes tight bounds for the Minimumweight Spanning Tree (MST) verification problem in the distributed setting. Specifically, we provide an MST verification algorithm that achieves simultaneously tilde ~O(E) messages and $tilde O(sqrt{n} + D) time, where E is the number of edges in the given graph G and D is G's diameter. On the negative side, we show that any MST verification algorithm must send Omega(E) messages and incur ~Omega(sqrt{n} + D) time in worst case.
Our upper bound result appears to indicate that the verification of an MST may be easier than its construction, since for MST construction, both lower bounds of Omega(E) messages and
Omega(sqrt{n} + D) time hold, but at the moment there is no known distributed algorithm that constructs an MST and achieves simultaneously tilde O(E) messages and ´~O(sqrt{n} + D) time. Specifically, the best known timeoptimal algorithm (using ~O(sqrt{n} + D) time) requires O(E+n^{3/2}) messages, and the best known messageoptimal algorithm (using ~O(E) messages) requires O(n) time.
On the other hand, our lower bound results indicate that the verification of an MST is not significantly easier than its construction.
BibTeX  Entry
@InProceedings{kor_et_al:LIPIcs:2011:3000,
author = {Liah Kor and Amos Korman and David Peleg},
title = {{Tight Bounds For Distributed MST Verification}},
booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
pages = {6980},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897255},
ISSN = {18688969},
year = {2011},
volume = {9},
editor = {Thomas Schwentick and Christoph D{\"u}rr},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2011/3000},
URN = {urn:nbn:de:0030drops30000},
doi = {http://dx.doi.org/10.4230/LIPIcs.STACS.2011.69},
annote = {Keywords: distributed algorithms, distributed verification, labeling schemes, minimumweight spanning tree}
}
Keywords: 

distributed algorithms, distributed verification, labeling schemes, minimumweight spanning tree 
Seminar: 

28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Issue date: 

2011 
Date of publication: 

11.03.2011 