{"file_date_updated":"2018-03-15T06:35:58Z","date_updated":"2022-01-06T07:03:01Z","citation":{"ama":"Kolman P, Scheideler C. Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case. In: *Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)*. ; 2012:800-810. doi:10.1137/1.9781611973099.64","chicago":"Kolman, Petr, and Christian Scheideler. “Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case.” In *Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)*, 800–810, 2012. https://doi.org/10.1137/1.9781611973099.64.","ieee":"P. Kolman and C. Scheideler, “Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case,” in *Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)*, 2012, pp. 800–810.","short":"P. Kolman, C. Scheideler, in: Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA), 2012, pp. 800–810.","apa":"Kolman, P., & Scheideler, C. (2012). Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case. In *Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)* (pp. 800–810). https://doi.org/10.1137/1.9781611973099.64","bibtex":"@inproceedings{Kolman_Scheideler_2012, title={Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case}, DOI={10.1137/1.9781611973099.64}, booktitle={Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)}, author={Kolman, Petr and Scheideler, Christian}, year={2012}, pages={800–810} }","mla":"Kolman, Petr, and Christian Scheideler. “Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case.” *Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)*, 2012, pp. 800–10, doi:10.1137/1.9781611973099.64."},"status":"public","page":"800-810","user_id":"15504","ddc":["040"],"publication":"Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)","date_created":"2017-10-17T12:42:55Z","has_accepted_license":"1","project":[{"name":"SFB 901","_id":"1"},{"name":"SFB 901 - Subprojekt A1","_id":"5"},{"_id":"2","name":"SFB 901 - Project Area A"}],"type":"conference","author":[{"last_name":"Kolman","full_name":"Kolman, Petr","first_name":"Petr"},{"id":"20792","first_name":"Christian","full_name":"Scheideler, Christian","last_name":"Scheideler"}],"year":"2012","file":[{"file_id":"1234","file_name":"632-SODA2012-Scheideler_01.pdf","date_updated":"2018-03-15T06:35:58Z","relation":"main_file","access_level":"closed","success":1,"content_type":"application/pdf","creator":"florida","file_size":220213,"date_created":"2018-03-15T06:35:58Z"}],"_id":"632","title":"Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case","abstract":[{"text":"Given an integer h, a graph G = (V;E) with arbitrary positive edge capacities and k pairs of vertices (s1; t1); (s2; t2); : : : ; (sk; tk), called terminals, an h-route cut is a set F µ E of edges such that after the removal of the edges in F no pair si ¡ ti is connected by h edge-disjoint paths (i.e., the connectivity of every si ¡ ti pair is at most h ¡ 1 in (V;E n F)). The h-route cut is a natural generalization of the classical cut problem for multicommodity °ows (take h = 1). The main result of this paper is an O(h722h log2 k)-approximation algorithm for the minimum h-route cut problem in the case that s1 = s2 = ¢ ¢ ¢ = sk, called the single source case. As a corollary of it we obtain an approximate duality theorem for multiroute multicom-modity °ows and cuts with a single source. This partially answers an open question posted in several previous papers dealing with cuts for multicommodity multiroute problems.","lang":"eng"}],"doi":"10.1137/1.9781611973099.64","department":[{"_id":"79"}]}