{"ddc":["040"],"date_updated":"2022-01-06T07:01:21Z","status":"public","title":"Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing","abstract":[{"text":"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.","lang":"eng"}],"author":[{"first_name":"Petr","last_name":"Kolman","full_name":"Kolman, Petr"},{"first_name":"Christian","full_name":"Scheideler, Christian","last_name":"Scheideler","id":"20792"}],"project":[{"name":"SFB 901","_id":"1"},{"name":"SFB 901 - Subprojekt A1","_id":"5"},{"_id":"2","name":"SFB 901 - Project Area A"}],"file":[{"file_size":264308,"relation":"main_file","date_updated":"2018-03-15T14:07:18Z","creator":"florida","file_name":"476-tocsrevised3b.pdf","access_level":"closed","file_id":"1326","date_created":"2018-03-15T14:07:18Z","success":1,"content_type":"application/pdf"}],"citation":{"chicago":"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. https://doi.org/10.1007/s00224-013-9454-3.","mla":"Kolman, Petr, and Christian Scheideler. “Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing.” *Theory of Computing Systems*, no. 2, Springer, 2013, pp. 341–63, doi:10.1007/s00224-013-9454-3.","ieee":"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.","ama":"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","apa":"Kolman, P., & Scheideler, C. (2013). Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing. *Theory of Computing Systems*, (2), 341–363. https://doi.org/10.1007/s00224-013-9454-3","short":"P. Kolman, C. Scheideler, Theory of Computing Systems (2013) 341–363.","bibtex":"@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} }"},"has_accepted_license":"1","type":"journal_article","page":"341-363","issue":"2","publication":"Theory of Computing Systems","date_created":"2017-10-17T12:42:24Z","_id":"476","department":[{"_id":"79"}],"file_date_updated":"2018-03-15T14:07:18Z","doi":"10.1007/s00224-013-9454-3","publisher":"Springer","year":"2013","user_id":"477"}