Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Finding minimum-quotient cuts in planar graphs
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
SIAM Journal on Discrete Mathematics
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Decision algorithms for unsplittable flow and the half-disjoint paths problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximations for the disjoint paths problem in high-diameter planar networks
Journal of Computer and System Sciences
Improved bounds for all optical routing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A polynomial-time tree decomposition to minimize congestion
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Constant factor approximation of vertex-cuts in planar graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Multicommodity Flow and Circuit Switching
HICSS '98 Proceedings of the Thirty-First Annual Hawaii International Conference on System Sciences-Volume 7 - Volume 7
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
A note on the greedy algorithm for the unsplittable flow problem
Information Processing Letters
Journal of Computer and System Sciences
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On Multidimensional Packing Problems
SIAM Journal on Computing
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Edge-Disjoint Paths in Planar Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The equivalence of theorem proving and the interconnection problem
ACM SIGDA Newsletter
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Oblivious routing on node-capacitated and directed graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Truthful and Near-Optimal Mechanism Design via Linear Programming
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An Approximation Algorithm for the Disjoint Paths Problem in Even-Degree Planar Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Edge-disjoint paths in Planar graphs with constant congestion
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New hardness results for congestion minimization and machine scheduling
Journal of the ACM (JACM)
Hardness of routing with congestion in directed graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A nearly linear time algorithm for the half integral disjoint paths packing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Disjoint paths in sparse graphs
Discrete Applied Mathematics
Flow-cut gaps for integer and fractional multiflows
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Improved algorithm for the half-disjoint paths problem
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Edge Disjoint Paths in Moderately Connected Graphs
SIAM Journal on Computing
The disjoint paths problem: algorithm and structure
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Breaking o(n1/2)-approximation algorithms for the edge-disjoint paths problem with congestion two
Proceedings of the forty-third annual ACM symposium on Theory of computing
An algorithm for the graph crossing number problem
Proceedings of the forty-third annual ACM symposium on Theory of computing
Truthful and Near-Optimal Mechanism Design via Linear Programming
Journal of the ACM (JACM)
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Edge disjoint paths in moderately connected graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
On vertex sparsifiers with Steiner nodes
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximation algorithms and hardness of integral concurrent flow
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Routing in undirected graphs with constant congestion
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Flow-cut gaps for integer and fractional multiflows
Journal of Combinatorial Theory Series B
An O(log n)-Approximation Algorithm for the Edge-Disjoint Paths Problem in Eulerian Planar Graphs
ACM Transactions on Algorithms (TALG)
Truthfulness and stochastic dominance with monetary transfers
Proceedings of the fourteenth ACM conference on Electronic commerce
Large-treewidth graph decompositions and applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Maximum edge-disjoint paths in k-sums of graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We study multicommodity routing problems in both edge and node capacitated undirected graphs. The input to each problem is a capacitated graph G=(V,E) and a set Τ of node pairs. In the simplest setting, the goal is to route a unit of flow for as many pairs as possible subject to the edge (node) capacity constraints. If the flow for a routed pair is required to be along a single path, it is the well-studied disjoint paths problem. If we allow fractional routings of the flow, it is known as the all-or-nothing flow problem. The nodes in Τ are referred to as terminals.In recent work [8,9], the authors obtained the first poly-logarithmic approximation algorithms for some edge routing problems. A key idea in these algorithms is to decompose an instance into a collection of instances in which the terminals are well-linked. Informally speaking, a set of nodes is well-linked in a graph if it does not have small separators. A decomposition into well-linked instances was previously achieved in [8] via räcke's hierarchical graph decomposition for oblivious routing [32]. In this paper, we design a simple new decomposition algorithm that is based on computing sparse cuts in a graph. Our new algorithm improves the earlier results for edge routing problems. Another important advantage of the algorithm is that it also applies to node-capacitated problems. We note that for oblivious routing with node capacities, an Ω√n) lower bound is known on the congestion [18], and hence the oblivious routing approach cannot yield poly-logarithmic bounds for well-linked decompositions. Using the new decomposition, we obtain a poly-logarithmic approximation for the node capacitated all-or-nothing flow problem in general graphs and node-disjoint path problem in planar graphs with O(1) congestion. We also show that the flow-cut gap for product multicommodity flows in node capacitated planar graphs is O(1), improving upon the O(log n) bound from [28].