On optimal realizations of finite metric spaces by graphs
Discrete & Computational Geometry
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A new way to weigh Malnourished Euclidean graphs
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Timing model reduction for hierarchical timing analysis
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Speeding up algorithms on compressed web graphs
Proceedings of the Second ACM International Conference on Web Search and Data Mining
Speeding up graph clustering via modular decomposition based compression
Proceedings of the 28th Annual ACM Symposium on Applied Computing
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We are given a graph with edge weights, that represents the metric on the vertices in which the distance between two vertices is the total weight of the lowest-weight path between them. Consider the problem of representing this metric using as few edges as possible, provided that new "steiner" vertices (and edges incident on them) can be added. The compression factor achieved is the ratio k between the number of edges in the original graph and the number of edges in the compressed graph. We obtain approximation algorithms for unit weight graphs that replace cliques with stars in cases where the cliques so compressed are disjoint, or when only a constant number of the cliques compressed meet at any vertex. We also show that the general unit weight problem is essentially as hard to approximate as graph coloring and maximum clique.