Estimating the weight of metric minimum spanning trees in sublinear-time

Authors

Artur Czumaj, Department of Computer Science
Christian Sohler, Department of Computer Science

Document Type

Conference Proceeding

Publication Date

1-1-2004

Abstract

In this paper we present a sublinear time (1 + ε)-approxima-tion randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is ̃ script o sign (n/ε^{script o sign (1)}). Since the full description of an n-point metric space is of size Θ(n²), 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. Furthermore, it has been previously shown that no o(n² algorithm exists that returns a spanning tree whose weight is within a constant times the optimum.

Identifier

4544232361 (Scopus)

Publication Title

Conference Proceedings of the Annual ACM Symposium on Theory of Computing

External Full Text Location

https://doi.org/10.1145/1007352.1007386

ISSN

07349025

First Page

175

Last Page

183

Recommended Citation

Czumaj, Artur and Sohler, Christian, "Estimating the weight of metric minimum spanning trees in sublinear-time" (2004). Faculty Publications. 20599.
https://digitalcommons.njit.edu/fac_pubs/20599