Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

P. Kolman, C. Scheideler, Theory of Computing Systems (2013) 341.

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An elementary h-route ow, for an integer h 1, is a set of h edge- disjoint paths between a source and a sink, each path carrying a unit of ow, and an h-route ow is a non-negative linear combination of elementary h-routeows. An h-route cut is a set of edges whose removal decreases the maximum h-route ow between a given source-sink pair (or between every source-sink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity h-route cuts and ows, for h 3: The size of a minimum h-route cut is at least f=h and at most O(log4 k f) where f is the size of the maximum h-routeow and k is the number of commodities. The main step towards the proof of this duality is the design and analysis of a polynomial-time approximation algorithm for the minimum h-route cut problem for h = 3 that has an approximation ratio of O(log4 k). Previously, polylogarithmic approximation was known only for h-route cuts for h 2. A key ingredient of our algorithm is a novel rounding technique that we call multilevel ball-growing. Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity ows and cuts. Similar results are shown also for the sparsest multiroute cut problem.
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Theory of Computing Systems
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2
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341-363
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Kolman P, Scheideler C. Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing. Theory of Computing Systems. 2013;(2):341-363. doi:10.1007/s00224-013-9454-3.
Kolman, P., & Scheideler, C. (2013). Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing. Theory of Computing Systems, (2), 341–363. http://doi.org/10.1007/s00224-013-9454-3
@article{Kolman_Scheideler_2013, title={Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing}, DOI={10.1007/s00224-013-9454-3}, number={2}, journal={Theory of Computing Systems}, publisher={Springer}, author={Kolman, Petr and Scheideler, Christian}, year={2013}, pages={341–363}}
Kolman, Petr, and Christian Scheideler. “Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing.” Theory of Computing Systems, no. 2 (2013): 341–63. doi:10.1007/s00224-013-9454-3.
P. Kolman and C. Scheideler, “Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing,” Theory of Computing Systems, no. 2, pp. 341–363, 2013.
Kolman, Petr, and Christian Scheideler. “Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing.” Theory of Computing Systems 2 (2013): 341–363. Web.
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