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Routing in Networks with Low Doubling Dimension
ICDCS '06 Proceedings of the 26th IEEE International Conference on Distributed Computing Systems
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A nearly optimal oracle for avoiding failed vertices and edges
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Fault-tolerant compact routing schemes for general graphs
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STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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
Fault-tolerant compact routing schemes for general graphs
Information and Computation
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The paper proposes a forbidden-set labeling scheme for the family of graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ε 0, the labeling scheme stores an O(1+α-1)2α log2 n-bit label at each vertex. Given the labels of two end-vertices s and t, and the labels of a set F of "forbidden" vertices and/or edges, our scheme can compute, in time polynomial in the length of the labels, a 1+ε stretch approximation for the distance between s and t in the graph GF. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ε for graphs of bounded doubling dimension.