A case for end system multicast (keynote address)
Proceedings of the 2000 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Scalable application layer multicast
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Representing Graph Metrics with Fewest Edges
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Minimum Restricted Diameter Spanning Trees
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximate classification via earthmover metrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum restricted diameter spanning trees
Discrete Applied Mathematics
Lower bounds for graph embeddings and combinatorial preconditioners
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A tight upper bound on the probabilistic embedding of series-parallel graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Assign ranges in general ad-hoc networks
Journal of Parallel and Distributed Computing - Special issue: Algorithms for wireless and ad-hoc networks
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Reconstructing approximate tree metrics
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the treeness of internet latency and bandwidth
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems
ACM Transactions on Algorithms (TALG)
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Vertex sparsifiers: new results from old techniques
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
A Tight Upper Bound on the Probabilistic Embedding of Series-Parallel Graphs
SIAM Journal on Discrete Mathematics
Narrow-Shallow-Low-Light Trees with and without Steiner Points
SIAM Journal on Discrete Mathematics
Assign ranges in general ad-hoc networks
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
A tight lower bound for the steiner point removal problem on trees
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
A note on the subadditive network design problem
Operations Research Letters
Theoretical Computer Science
Preserving terminal distances using minors
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Consider an edge-weighted tree T = (V, E, w : E ↣ R+), in which a subset R of the nodes (called the required nodes) are colored red and the remaining nodes in S = V\R are colored black (and called the Steiner nodes). The shortest-path distance according to the edge-weights defines a metric dT on the vertex set V.We now ask the following question: Is it possible to define another weighted tree T* = (R, E*, w* : E* ↣ R+), this time on just the red vertices so that the shortest-path metric dT* induced by T* on the vertices in R is “close” to the metric dT restricted to the red vertices? I.e., does there exist a weighted tree T* = (R, E*, c*) and a (small) constant &agr; such that dT(u, v) ≤ dT* (u, v) ≤ &agr; dT(u, v) for any two red vertices u, v ∈ R?We answer this question in the affirmative, and give a linear time algorithm to obtain a tree T* with &agr; ≤ 8. We also give two applications of this result: an upper bound, in which we show that emulating multicasts using unicasts can be almost as good as general multicasts for certain performance measures; and a lower bound, in which we give a simple combinatorial proof of the fact that the metric generated by a graph of girthg must suffer a distortion of at least &OHgr;(g) when approximated by a tree.