Constrained-Path Labellings on Graphs of Bounded Clique-Width

Given a graph G we consider the problem of preprocessing it so that given two vertices x,y and a set X of vertices, we can efficiently report the shortest path (or just its length) between x,y that avoids X. We attach labels to vertices in such a way that this length can be determined from the labels of x,y and the vertices X. For a graph with n vertices of tree-width or clique-width k, we construct labels of size O(k2 log2 n). The constructions extend to directed graphs. The problem is motivated by routing in networks in case of failures or of routing policies which forbid certain paths. Keywords Algorithms · Labelling schemes · Compact routing · Clique-width

• Type: Journal
• Year: 2010
• Where: MST
• Authors: Bruno Courcelle, Andrew Twigg
• Keywords: Labels, MST 2010, Routing, Vertices X