Collective Tree Spanners and Routing in AT-free Related Graphs

In this paper we study collective additive tree spanners for families of graphs that either contain or are contained in AT-free graphs. We say that a graph G = (V, E) admits a system of µ collective additive tree rspanners if there is a system T (G) of at most µ spanning trees of G such that for any two vertices x, y of G a spanning tree T ∈ T (G) exists such that dT (x, y) ≤ dG(x, y) + r. Among other results, we show that AT-free graphs have a system of two collective additive tree 2-spanners (whereas there are trapezoid graphs that do not admit any additive tree 2-spanner). Furthermore, based on this collection, we derive a compact and efficient routing scheme. Also, any DSP-graph (there exists a dominating shortest path) admits an additive tree 4-spanner, a system of two collective additive tree 3-spanners and a system of five collective additive tree 2-spanners. Article Type Communicated by Submitted Revised regular paper S. Khuller January 2005 January 2006 Results of this...

• Type: Conference
• Year: 2004
• Where: WG
• Authors: Feodor F. Dragan, Chenyu Yan, Derek G. Corneil
• Keywords: Additive Tree 2-spanners, Additive Tree Spanners, Collective Additive Tree, Computer Science, WG 2004