2026-07-23T07:58:23Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:1358 2024-03-06T10:32:59Z ddc:004 open_access

Computing Minimum Spanning Trees with Uncertainty Hoffmann, Michael Erlebach, Thomas Krizanc, Danny Mihal'ák, Matús Raman, Rajeev Algorithms and data structures; Current challenges: mobile and net computing 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 $A_e$, called an uncertainty area, that contains the actual edge weight $w_e$ is known. The algorithm can `update' $e$ to obtain the edge weight $w_e in A_e$. 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 $A_e$ are open or trivial, which is the best possible among deterministic algorithms. The condition on the areas $A_e$ 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Michael Hoffmann and Thomas Erlebach and Danny Krizanc and Matús Mihal'ák and Rajeev Raman 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1358 urn:nbn:de:0030-drops-13581 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1358 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode