Journal of Combinatorial Theory Series B
Powers of distance-hereditary graphs
Discrete Mathematics
European Journal of Combinatorics - Special issue on discrete metric spaces
Regular Article: Trees, Taxonomy, and Strongly Compatible Multi-state Characters
Advances in Applied Mathematics
Retractions of finite distance functions onto tree metrics
Discrete Applied Mathematics
On the approximability of numerical taxonomy (fitting distances by tree metrics)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
European Journal of Combinatorics
SIAM Journal on Discrete Mathematics
Labeling schemes for small distances in trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Distance Labeling Schemes
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Journal of Algorithms
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Traveling with a Pez Dispenser (or, Routing Issues in MPLS)
SIAM Journal on Computing
Fast construction of nets in low dimensional metrics, and their applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Distance and routing labeling schemes for non-positively curved plane graphs
Journal of Algorithms
Proximity-preserving labeling schemes
Journal of Graph Theory
Query efficient implementation of graphs of bounded clique-width
Discrete Applied Mathematics
On triangulation of simple networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Reconstructing approximate tree metrics
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Packing and Covering δ-Hyperbolic Spaces by Balls
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Distributed relationship schemes for trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Computing the hyperbolicity constant
Computers & Mathematics with Applications
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A graph G is δ-hyperbolic if for any four vertices u,v,x,y of G the two larger of the three distance sums dG(u,v) + dG(x,y), dG(u,x) + dG(v,y), dG(u,y) + dG(v,x) differ by at most δ, and the smallest δ ≥ 0 for which G is δ-hyperbolic is called the hyperbolicity of G. In this paper, we construct a distance labeling scheme for bounded hyperbolicity graphs, that is a vertex labeling such that the distance between any two vertices of G can be estimated from their labels, without any other source of information. More precisely, our scheme assigns labels of O(log2n) bits for bounded hyperbolicity graphs with n vertices such that distances can be approximated within an additive error of O(log n). The label length is optimal for every additive error up to nε. We also show a lower bound of Ω(log log n) on the approximation factor, namely every s-multiplicative approximate distance labeling scheme on bounded hyperbolicity graphs with polylogarithmic labels requires s = Ω(log log n).