Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
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
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
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)
A nearly linear time algorithm for the half integral disjoint paths packing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Systems Architecture: the EUROMICRO Journal
A nearly linear time algorithm for the half integral parity disjoint paths packing problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Disjoint paths in sparse graphs
Discrete Applied Mathematics
The edge disjoint paths problem in Eulerian graphs and 4-edge-connected graphs
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
Edge Disjoint Paths in Moderately Connected Graphs
SIAM Journal on Computing
Finding multiple induced disjoint paths in general graphs
Information Processing Letters
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
An O(log n)-Approximation Algorithm for the Edge-Disjoint Paths Problem in Eulerian Planar Graphs
ACM Transactions on Algorithms (TALG)
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 the maximum edge-disjoint paths problem (MEDP). We are given a graph G = (V,E) and a set T = {s1t1, s2t2, . . . , sktk} of pairs of vertices: the objective is to find the maximum number of pairs in T that can be connected via edge-disjoint paths. Our main result is a poly-logarithmic approximation for MEDP on undirected planar graphs if a congestion of 2 is allowed, that is, we allow up to 2 paths to share an edge. Prior to our work, for any constant congestion, only a polynomial-factor approximation was known for planar graphs although much stronger results are known for some special cases such as grids and grid-like graphs. We note that the natural multi-commodity flow relaxation of the problem has an integrality gap of \Omega (\sqrt {\left| V \right|} ) even on planar graphs when no congestion is allowed. Our starting point is the same relaxation and our result implies that the integrality gap shrinks to a poly-logarithmic factor once 2 paths are allowed per edge. Our result also extends to the unsplittable flow problem and the maximum integer multicommodity flow problem. A set X 驴 V is well-linked if for each S 驴 V , |驴(S)| 驴 min-{|S 驴 X|, |(V - S) 驴 X|}. The heart of our approach is to show that in any undirected planar graph, given any matching M on a well-linked set X, we can route 驴(|M|) pairs in M with a congestion of 2. Moreover, all pairs in M can be routed with constant congestion for a sufficiently large constant. This results also yields a different proof of a theorem of Klein, Plotkin, and Rao that shows an O(1) maxflow-mincut gap for uniform multicommodity flow instances in planar graphs. The framework developed in this paper applies to general graphs as well. If a certain graph theoretic conjecture is true, it will yield poly-logarithmic integrality gap for MEDP with constant congestion.