The maximum concurrent flow problem
Journal of the ACM (JACM)
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Towards a syntactic characterization of PTAS
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth 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
A lower bound on the distortion of embedding planar metrics into Euclidean space
Proceedings of the eighteenth annual symposium on Computational geometry
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th 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
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On average distortion of embedding metrics into the line and into L1
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Improved embeddings of graph metrics into random trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A simpler algorithm and shorter proof for the graph minor decomposition
Proceedings of the forty-third annual ACM symposium on Theory of computing
Bandwidth and low dimensional embedding
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Embedding bounded bandwidth graphs into ℓ1
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
Bandwidth and low dimensional embedding
Theoretical Computer Science
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We show that the shortest-path metric of any k-outerplanar graph, for any fixed k, can be approximated by a probability distribution over tree metrics with constant distortion, and hence also embedded into l1 with constant distortion. These graphs play a central role in polynomial time approximation schemes for many NP-hard optimization problems on general planar graphs, and include the family of weighted k × n planar grids.This result implies a constant upper bound on the ratio between the sparsest cut and the maximum concurrent flow in multicommodity networks for k-outerplanar graphs, thus extending a classical theorem of Okamura and Seymour [26] for outerplanar graphs, and of Gupta et al. [17] for treewidth-2 graphs. In addition, we obtain improved approximation ratios for k-outerplanar graphs on various problems for which approximation algorithms are based on probabilistic tree embeddings. We also conjecture that our random tree embeddings for k-outerplanar graphs can serve as a building block for more powerful l1 embeddings in future.