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| Description
| - An elementary h-route flow, for an integer ha parts per thousand yen1, is a set of h edge-disjoint paths between a source and a sink, each path carrying a unit of flow, and an h-route flow is a non-negative linear combination of elementary h-route flows. An h-route cut is a set of edges whose removal decreases the maximum h-route flow 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 flows, for ha parts per thousand currency sign3: The size of a minimum h-route cut is at least f/h and at most O(log(4) ka <...f) where f is the size of the maximum h-route flow 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(log(4) k). Previously, polylogarithmic approximation was known only for h-route cuts for ha parts per thousand currency sign2. 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 flows and cuts. Similar results are shown also for the sparsest multiroute cut problem.
- An elementary h-route flow, for an integer ha parts per thousand yen1, is a set of h edge-disjoint paths between a source and a sink, each path carrying a unit of flow, and an h-route flow is a non-negative linear combination of elementary h-route flows. An h-route cut is a set of edges whose removal decreases the maximum h-route flow 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 flows, for ha parts per thousand currency sign3: The size of a minimum h-route cut is at least f/h and at most O(log(4) ka <...f) where f is the size of the maximum h-route flow 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(log(4) k). Previously, polylogarithmic approximation was known only for h-route cuts for ha parts per thousand currency sign2. 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 flows and cuts. Similar results are shown also for the sparsest multiroute cut problem. (en)
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| Title
| - Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
- Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing (en)
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| skos:prefLabel
| - Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
- Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing (en)
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| skos:notation
| - RIV/00216208:11320/13:10159252!RIV14-GA0-11320___
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...iv/cisloPeriodika
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/13:10159252
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - Duality; Approximation algorithms; Multicommodity flow (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...odStatuVydavatele
| - DE - Spolková republika Německo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/nazevZdroje
| - Theory of Computing Systems
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...v/svazekPeriodika
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| http://linked.open...iv/tvurceVysledku
| - Kolman, Petr
- Scheideler, Christian
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| http://linked.open...ain/vavai/riv/wos
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| issn
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| number of pages
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| http://bibframe.org/vocab/doi
| - 10.1007/s00224-013-9454-3
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| http://localhost/t...ganizacniJednotka
| |
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