{"file":[{"content_type":"application/pdf","access_level":"closed","file_size":220213,"creator":"florida","relation":"main_file","file_id":"1234","date_updated":"2018-03-15T06:35:58Z","success":1,"file_name":"632-SODA2012-Scheideler_01.pdf","date_created":"2018-03-15T06:35:58Z"}],"file_date_updated":"2018-03-15T06:35:58Z","status":"public","department":[{"_id":"79"}],"date_updated":"2022-01-06T07:03:01Z","doi":"10.1137/1.9781611973099.64","ddc":["040"],"_id":"632","project":[{"name":"SFB 901","_id":"1"},{"_id":"5","name":"SFB 901 - Subprojekt A1"},{"name":"SFB 901 - Project Area A","_id":"2"}],"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"}],"date_created":"2017-10-17T12:42:55Z","title":"Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case","page":"800-810","has_accepted_license":"1","publication":"Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)","author":[{"first_name":"Petr","last_name":"Kolman","full_name":"Kolman, Petr"},{"first_name":"Christian","full_name":"Scheideler, Christian","last_name":"Scheideler","id":"20792"}],"user_id":"15504","type":"conference","year":"2012","citation":{"chicago":"Kolman, Petr, and Christian Scheideler. “Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case.” In <i>Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)</i>, 800–810, 2012. <a href=\"https://doi.org/10.1137/1.9781611973099.64\">https://doi.org/10.1137/1.9781611973099.64</a>.","mla":"Kolman, Petr, and Christian Scheideler. “Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case.” <i>Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)</i>, 2012, pp. 800–10, doi:<a href=\"https://doi.org/10.1137/1.9781611973099.64\">10.1137/1.9781611973099.64</a>.","short":"P. Kolman, C. Scheideler, in: Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA), 2012, pp. 800–810.","apa":"Kolman, P., &#38; Scheideler, C. (2012). Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case. In <i>Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)</i> (pp. 800–810). <a href=\"https://doi.org/10.1137/1.9781611973099.64\">https://doi.org/10.1137/1.9781611973099.64</a>","ieee":"P. Kolman and C. Scheideler, “Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case,” in <i>Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)</i>, 2012, pp. 800–810.","ama":"Kolman P, Scheideler C. Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case. In: <i>Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)</i>. ; 2012:800-810. doi:<a href=\"https://doi.org/10.1137/1.9781611973099.64\">10.1137/1.9781611973099.64</a>","bibtex":"@inproceedings{Kolman_Scheideler_2012, title={Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case}, DOI={<a href=\"https://doi.org/10.1137/1.9781611973099.64\">10.1137/1.9781611973099.64</a>}, booktitle={Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)}, author={Kolman, Petr and Scheideler, Christian}, year={2012}, pages={800–810} }"}}