Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
The Computer Journal
Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Clin d'oeil on L1-embeddable planar graphs
Discrete Applied Mathematics - Special issue: 50th anniversary of the Wiener index
Theoretical Computer Science
Decomposition and l1-embedding of weakly median graphs
European Journal of Combinatorics
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Interval routing in some planar networks
Theoretical Computer Science
Coding the vertexes of a graph
IEEE Transactions on Information Theory
European Journal of Combinatorics
Distributed relationship schemes for trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Combinatorics and Geometry of Finite and Infinite Squaregraphs
SIAM Journal on Discrete Mathematics
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Localized and compact data-structure for comparability graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Compact routing for graphs excluding a fixed minor
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Convex Excess in Partial Cubes
Journal of Graph Theory
Shortest path problem in rectangular complexes of global nonpositive curvature
Computational Geometry: Theory and Applications
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Distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the distance between any two vertices u and v can be determined efficiently (e.g., in constant or logarithmic time) by merely inspecting the labels of u and v, without using any other information. Similarly, routing labeling schemes are schemes that label the vertices of a graph with short labels in such a way that given the label of a source vertex and the label of a destination, it is possible to compute efficiently (e.g., in constant or logarithmic time) the port number of the edge from the source that heads in the direction of the destination. In this paper we show that the three major classes of non-positively curved plane graphs enjoy such distance and routing labeling schemes using O(log^2n) bit labels on n-vertex graphs. In constructing these labeling schemes interesting metric properties of those graphs are employed.