On Interval Routing Schemes and Treewidth

Abstract. In this paper, we investigate which processor networks allow klabel Interval Routing Schemes, under the assumption that costs of edges may vary. We show that for each xed k  1, the class of graphs allowing such routing schemes is closed under minor-taking in the domain of connected graphs, and hence has a linear time recognition algorithm. This result connects the theory of compact routing with the theory of graph minors and treewidth. We show that every graph that does not contain K2;r as a minor has treewidth at most 2r , 2. In case the graph is planar, this bound can be lowered to r + 2. As a consequence, graphs that allow k-label Interval Routing Schemes under dynamic cost edges have treewidth at most 4k, and treewidth at most 2k+ 3 if they are planar. Similar results are shown for other types of Interval Routing Schemes.

• Type: Conference
• Year: 1995
• Where: WG
• Authors: Hans L. Bodlaender, Richard B. Tan, Dimitrios M. Thilikos, Jan van Leeuwen
• Keywords: Interval Routing Schemes, Networks Allow Klabel, Routing, Theoretical Computer Science, WG 1995