A fast distributed approximation algorithm for minimum spanning trees

We present a distributed algorithm that constructs an O (log n )-approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ( D ( G ) + L ( G , w )) where L ( G , w ) is a parameter called the local shortest path diameter and D ( G ) is the (unweighted) diameter o...

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Bibliographic Details
Published in:Distributed computing Vol. 20; no. 6; pp. 391 - 402
Main Authors: Khan, Maleq, Pandurangan, Gopal
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.04.2008
Springer Nature B.V
Subjects:
Computer Communication Networks
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Software Engineering/Programming and Operating Systems
Theory of Computation
Distributed approximation algorithm
Randomized algorithm
Minimum spanning tree
ISSN:0178-2770, 1432-0452
Online Access:Get full text
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Summary:We present a distributed algorithm that constructs an O (log n )-approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ( D ( G ) + L ( G , w )) where L ( G , w ) is a parameter called the local shortest path diameter and D ( G ) is the (unweighted) diameter of the graph. Our algorithm is existentially optimal (up to polylogarithmic factors), i.e., there exist graphs which need Ω( D ( G ) + L ( G , w )) time to compute an H -approximation to the MST for any . Our result also shows that there can be a significant time gap between exact and approximate MST computation: there exists graphs in which the running time of our approximation algorithm is exponentially faster than the time-optimal distributed algorithm that computes the MST. Finally, we show that our algorithm can be used to find an approximate MST in wireless networks and in random weighted networks in almost optimal Õ( D ( G )) time.
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ISSN:0178-2770
1432-0452
DOI:10.1007/s00446-007-0047-8