TY - GEN

T1 - A node-capacitated okamura-seymour theorem

AU - Lee, James R.

AU - Mendel, Manor

AU - Moharrami, Mohamad

PY - 2013

Y1 - 2013

N2 - The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are satisfied. Simple examples show that a similar theorem is impossible in the node-capacitated setting. Nevertheless, we prove that an approximate flow/cut theorem does hold: For some universal " ε > 0, if the node cut conditions are satisfied, then one can simultaneously route an " ε- fraction of all the demands. This answers an open question of Chekuri and Kawarabayashi. More generally, we show that this holds in the setting of multi-commodity polymatroid networks introduced by Chekuri, et. al. Our approach employs a new type of random metric embedding in order to round the convex programs corresponding to these more general flow problems.

AB - The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are satisfied. Simple examples show that a similar theorem is impossible in the node-capacitated setting. Nevertheless, we prove that an approximate flow/cut theorem does hold: For some universal " ε > 0, if the node cut conditions are satisfied, then one can simultaneously route an " ε- fraction of all the demands. This answers an open question of Chekuri and Kawarabayashi. More generally, we show that this holds in the setting of multi-commodity polymatroid networks introduced by Chekuri, et. al. Our approach employs a new type of random metric embedding in order to round the convex programs corresponding to these more general flow problems.

KW - Metric embeddings

KW - Multi-commodity flows

UR - http://www.scopus.com/inward/record.url?scp=84879835110&partnerID=8YFLogxK

U2 - 10.1145/2488608.2488671

DO - 10.1145/2488608.2488671

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AN - SCOPUS:84879835110

SN - 9781450320290

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 495

EP - 504

BT - STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing

T2 - 45th Annual ACM Symposium on Theory of Computing, STOC 2013

Y2 - 1 June 2013 through 4 June 2013

ER -