Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time

In this paper the authors present a sublinear-time (1+...)-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is ... Since the full description of an n-point metric space is of size ..., the complexity...

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Bibliographic Details
Published inSIAM journal on computing Vol. 39; no. 3; pp. 904 - 922
Main Authors Czumaj, Artur, Sohler, Christian
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Subjects
Algorithms
Approximation
Estimates
Internet Protocol
Linear equations
Metric space
Optimization
Randomized algorithms
Running
Studies
Symbols
Trees
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ISSN0097-5397
1095-7111
DOI10.1137/060672121

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Summary:In this paper the authors present a sublinear-time (1+...)-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is ... Since the full description of an n-point metric space is of size ..., the complexity of their algorithm is sublinear with respect to the input size. Their algorithm is almost optimal as it is not possible to approximate in o(n) time the weight of the minimum spanning tree to within any factor. They also show that no deterministic algorithm can achieve a B-approximation in ... time. Furthermore, it has been previously shown that no o(n^sup 2^) algorithm exists that returns a spanning tree whose weight is within a constant times the optimum. (ProQuest: ... denotes formulae/symbols omitted.)
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ISSN:0097-5397
1095-7111
DOI:10.1137/060672121