Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
Kolman, Petr
Scheideler, Christian
ddc:040
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.
Springer
2013
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://ris.uni-paderborn.de/record/476
Kolman P, Scheideler C. Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing. <i>Theory of Computing Systems</i>. 2013;(2):341-363. doi:<a href="https://doi.org/10.1007/s00224-013-9454-3">10.1007/s00224-013-9454-3</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00224-013-9454-3
info:eu-repo/semantics/closedAccess