Compact labelings for efficient first-order model-checking
Journal of Combinatorial Optimization
Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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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.