Vertex sparsifiers : new results from old techniques
Englert, Matthias, Gupta, Anupam (Researcher in Computer Science), Krauthgamer, Robert, Raecke, Harald, Talgam-Cohen, Inbal and Talwar, Kunal (2010) Vertex sparsifiers : new results from old techniques. In: 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2010)/14th International Workshop on Randomization and Computation (RANDOM 2010), Univ Politecnica Catalunya (UPC), Barcelona, Spain, 01-03 Sep 2010Full text not available from this repository.
Given a capacitated graph G = (V, E) and a set of terminals K subset of V, how should we produce a graph H only on the terminals K so that every (multicommodity) flow between the terminals in G could be supported in H with low congestion, and vice versa? (Such a graph H is called a flow-sparsifier for G.) What if we want H to be a "simple" graph? What if we allow H to be a convex combination of simple graphs?
Improving on results of Moitra [FOCS 2009] and Leighton and Moitra [STOC 2010], we give efficient algorithms for constructing: (a) a flow-sparsifier H that maintains congestion up to a factor of O(log k/log log k), where k = vertical bar K vertical bar. (b) a convex combination of trees over the terminals K that maintains congestion up to a factor of O(log k). (c) for a planar graph G, a convex combination of planar graphs that maintains congestion up to a constant factor. This requires us to give a new algorithm for the 0-extension problem, the first one in which the preimages of each terminal are connected in G. Moreover, this result extends to minor-closed families of graphs.
Our bounds immediately imply improved approximation guarantees for several terminal-based cut and ordering problems.
|Item Type:||Conference Item (Paper)|
|Subjects:||Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software|
|Divisions:||Faculty of Science > Computer Science|
|Library of Congress Subject Headings (LCSH):||Computer terminals, Graph algorithms|
|Editor:||Serna, M and Shaltiel, R and Jansen, K and Rolim, J|
|Version or Related Resource:||Englert, Matthias, Gupta, A., Krauthgamer, Robert, Räcke, Harald, Talgam-Cohen, Inbal and Talwar, Kunal (2010) Vertex sparsifiers : new results from old techniques. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science (6302). Springer Verlag, pp. 152-165. ISBN 9783642153686 http://wrap.warwick.ac.uk/id/eprint/47422|
|Conference Paper Type:||Paper|
|Title of Event:||13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2010)/14th International Workshop on Randomization and Computation (RANDOM 2010)|
|Type of Event:||Workshop|
|Location of Event:||Univ Politecnica Catalunya (UPC), Barcelona, Spain|
|Date(s) of Event:||01-03 Sep 2010|
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