Abstract
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(k 2log 2 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.
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B. Courcelle was supported by the GRAAL project of “Agence Nationale pour la Recherche”.
This work was done under the support for A. Twigg by US Army Research Laboratory and UK Ministry of Defence grant W911NF-06-3-0001, and while at the Computer Laboratory, University of Cambridge.
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Courcelle, B., Twigg, A. Constrained-Path Labellings on Graphs of Bounded Clique-Width. Theory Comput Syst 47, 531–567 (2010). https://doi.org/10.1007/s00224-009-9211-9
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DOI: https://doi.org/10.1007/s00224-009-9211-9