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Implicit representation of graphs
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A trade-off between space and efficiency for routing tables
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Fast deterministic distributed algorithms for sparse spanners
Theoretical Computer Science
Polylogarithmic network navigability using compact metrics with small stretch
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Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
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Distributed relationship schemes for trees
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Forbidden-set distance labels for graphs of bounded doubling dimension
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Context-aware nearest neighbor query on social networks
SocInfo'11 Proceedings of the Third international conference on Social informatics
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SIAM Journal on Discrete Mathematics
Fast deterministic distributed algorithms for sparse spanners
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Distance labeling in hyperbolic graphs
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Localized and compact data-structure for comparability graphs
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Exact distance labelings yield additive-stretch compact routing schemes
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Compact routing for graphs excluding a fixed minor
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SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Shortest-path queries for complex networks: exploiting low tree-width outside the core
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Controller and estimator for dynamic networks
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Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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We consider the problem of labeling the nodes of a graph in a way that will allow one to compute the distance between any two nodes directly from their labels (without using any additional information). Our main interest is in the minimal length of labels needed in different cases. We obtain upper and lower bounds for several interesting families of graphs. In particular, our main results are the following. For general graphs, we show that the length needed is Θ(n). For trees, we show that the length needed is Θ(log2 n). For planar graphs, we show an upper bound of O(√nlogn) and a lower bound of Ω(n1/3). For bounded degree graphs, we show a lower bound of Ω(√n). The upper bounds for planar graphs and for trees follow by a more general upper bound for graphs with a r(n)-separator. The two lower bounds, however, are obtained by two different arguments that may be interesting in their own right. We also show some lower bounds on the length of the labels, even if it is only required that distances be approximated to a multiplicative factor s. For example, we show that for general graphs the required length is Ω(n) for every s n, such that if we use any labels with fewer than n bits per label, computing the distance function requires exponential time. A similar result is obtained for planar and bounded degree graphs.