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Estimating the weight of metric minimum spanning trees in sublinear time
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Czumaj, Artur and Sohler, Christian. (2009) Estimating the weight of metric minimum spanning trees in sublinear time. SIAM Journal on Computing, Vol.39 (No.3). pp. 904922. ISSN 00975397

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Official URL: http://dx.doi.org/10.1137/060672121
Abstract
In this paper we present a sublineartime $(1+\varepsilon)$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 $\widetilde{\mathcal{O}}(n/\varepsilon^{\mathcal{O}(1)})$. Since the full description of an $n$point metric space is of size $\Theta(n^2)$, the complexity of our algorithm is sublinear with respect to the input size. Our 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. We also show that no deterministic algorithm can achieve a $B$approximation in $o(n^2/B^3)$ time. Furthermore, it has been previously shown that no $o(n^2)$ algorithm exists that returns a spanning tree whose weight is within a constant times the optimum.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software  
Divisions:  Faculty of Science > Computer Science  
Library of Congress Subject Headings (LCSH):  Spanning trees (Graph theory), Estimation theory  Computer programs, Algorithms  
Journal or Publication Title:  SIAM Journal on Computing  
Publisher:  Society for Industrial and Applied Mathematics  
ISSN:  00975397  
Official Date:  26 August 2009  
Dates: 


Volume:  Vol.39  
Number:  No.3  
Page Range:  pp. 904922  
Identification Number:  10.1137/060672121  
Status:  Peer Reviewed  
Access rights to Published version:  Open Access  
References:  [1] N. Alon, S. Dar, M. Parnas, and D. Ron, Testing of clustering, SIAM J. Discrete Math., 

URI:  http://wrap.warwick.ac.uk/id/eprint/2416 
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