Computing Minimum Spanning Trees with Uncertainty

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 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...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Thomas Erlebach, Michael Hoffmann 0002, Danny Krizanc, Matús Mihalák, Rajeev Raman
• Keywords: Algorithms, Competitive Algorithm, CORR 2008, Edge, Education