Name
Abstract | ||
|---|---|---|
We consider the minimum spanning tree problem in a setting where informa,tion 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) is an element of 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. |
Year | Venue | Keywords |
|---|---|---|
2008 | STACS 2008: PROCEEDINGS OF THE 25TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE | algorithms and data structures,current challenges : mobile and net computing |
DocType | Volume | ISSN |
Journal | abs/0802.2855 | Dans Proceedings of the 25th Annual Symposium on the Theoretical
Aspects of Computer Science - STACS 2008, Bordeaux : France (2008) |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thomas Erlebach | 1 | 1233 | 102.74 |
| Michael Hoffmann 0002 | 2 | 62 | 7.23 |
| Danny Krizanc | 3 | 1778 | 191.04 |
| Matús Mihalák | 4 | 151 | 22.49 |
| Rajeev Raman | 5 | 1550 | 110.81 |