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# Computing Minimum Spanning Trees with Uncertainty

conference contribution

posted on 2013-09-10, 13:05 authored by Thomas Erlebach, Michael Hoffmann, Danny Krizanc, Matúš Mihal’ák, Rajeev RamanWe consider the minimum spanning tree problem in a setting where information about the edge weights of the given graph is uncertain. Initially, for each edge e of the graph only a set Aₑ, called an uncertainty area, that contains the actual edge weight wₑ is known. The algorithm can ‘update’ e to obtain the edge weight wₑ E Aₑ. The task is to output the edge set of a minimum spanning tree after a minimum number of updates.
An algorithm is k-update competitive if it makes at most k times as many updates as the optimum. We present a 2-update competitive algorithm if all areas Aₑ are open or trivial, which is the best possible among deterministic algorithms. The condition on the areas Aₑ is to exclude degenerate inputs for which no constant update competitive algorithm can exist.
Next, we consider a setting where the vertices of the graph correspond to points in Euclidean space and the weight of an edge is equal to the distance of its endpoints. The location of each point is initially given as an uncertainty area, and an update reveals the exact location of the point. We give a general relation between the edge uncertainty and the vertex uncertainty versions of a problem and use it to derive a 4-update competitive algorithm for the minimum spanning tree problem in the vertex uncertainty model. Again, we show that this is best possible among deterministic algorithms.

## History

## Citation

Erlebach, T., Hoffmann, M. et al. ‘Computing Minimum Spanning Trees with Uncertainty’ in Albers, S., Weil, P. (eds.) Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science (Copyright © 2008, the authors), pp. 277-288## Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science## Source

25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008), Bordeaux, France## Version

- VoR (Version of Record)

## Published in

Erlebach## Publisher

IBFI Schloss Dagstuhl## isbn

978-3-939897-06-4## Copyright date

2008## Available date

2013-09-10## Publisher version

http://stacs08.labri.fr/## Editors

Albers, S.;Weil, P.## Temporal coverage: start date

2008-02-21## Temporal coverage: end date

2008-02-23## Language

en## Administrator link

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