{
"id": "https://doi.org/10.4230/lipics.stacs.2011.129",
"doi": "10.4230/LIPICS.STACS.2011.129",
"url": "http://drops.dagstuhl.de/opus/volltexte/2011/3005/",
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"creators": [
{
"name": "Kolman, Petr",
"nameType": "Personal",
"givenName": "Petr",
"familyName": "Kolman",
"affiliation": []
},
{
"name": "Scheideler, Christian",
"nameType": "Personal",
"givenName": "Christian",
"familyName": "Scheideler",
"affiliation": []
}
],
"titles": [
{
"title": "Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing"
}
],
"publisher": "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany",
"container": {},
"subjects": [
{
"subject": "Computer Science"
},
{
"subject": "000 Computer science, knowledge, general works",
"subjectScheme": "DDC"
}
],
"contributors": [
{
"name": "Herbstritt, Marc",
"nameType": "Personal",
"givenName": "Marc",
"familyName": "Herbstritt",
"affiliation": [],
"contributorType": "Editor"
}
],
"dates": [
{
"date": "2011-03-11",
"dateType": "Available"
},
{
"date": "2011",
"dateType": "Issued"
}
],
"publicationYear": 2011,
"language": "eng",
"identifiers": [
{
"identifier": "https://doi.org/10.4230/lipics.stacs.2011.129",
"identifierType": "DOI"
}
],
"sizes": [
"12 pages"
],
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"application/pdf"
],
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"descriptions": [
{
"description": "An elementary h-route flow, 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 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\n$h$-route cuts and flows, for h <= 3: The size of a minimum h-route cut is at least f/h and at most O(log^3(k)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^3 k). Previously, polylogarithmic approximation was known only for $h$-route cuts for h <= 2.\nA 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.",
"descriptionType": "Other"
}
],
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