Please use this identifier to cite or link to this item: http://hdl.handle.net/2381/28154
Title: Computing Minimum Spanning Trees with Uncertainty
Authors: Erlebach, Thomas
Hoffmann, Michael
Krizanc, Danny
Mihal’ák, Matúš
Raman, Rajeev
First Published: 2008
Presented at: 25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008), Bordeaux, France
Start Date: 21-Feb-2008
End Date: 23-Feb-2008
Publisher: IBFI Schloss Dagstuhl
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
Abstract: We 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.
ISBN: 978-3-939897-06-4
Links: http://stacs08.labri.fr/
http://hdl.handle.net/2381/28154
Version: Publisher Version
Status: Peer-reviewed
Type: Conference Paper
Rights: Copyright © 2008, the authors. This work is licensed under the Creative Commons Attribution-NoDerivs License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nd/3.0/.
Appears in Collections:Conference Papers & Presentations, Dept. of Computer Science

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