Computing cut-based hierarchical decompositions in almost linear time

Harald Räcke, Chintan Shah, Hanjo Täubig

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

44 Zitate (Scopus)

Abstract

We present a fast construction algorithm for the hierarchical tree decompositions that lie at the heart of oblivious routing strategies and that form the basis for approximation and online algorithms for various cut problems in graphs. Given an undirected graph G = (V, E, c) with edge capacities, we compute a single tree T = (Vt,Et,Ct), where the leaf nodes of T correspond to nodes in G. such that the tree approximates the cut-structure of G up to a factor of O(log4 n). The best existing construction by Harrelson, Hildrum, and Rao [12] just guarantees a polynomial running time but offers a better approximation guarantee of O(log2 n log log n). Phrasing our results in terms of vertex sparsifiers, we obtain the following: For a graph G = (V, E) with a subset S of terminals, we compute a tree T with at most 2IS| vertices (and the leafs of T correspond to nodes in S) such that T is a flow-sparsifier for S in G with quality O(log2 nlog2 k), where |V| = n and |S| = k. The running time is O(polylog n . T(m, 1/log3 n)) where T(m, e) is the time for computing an approximate maxflow in a graph with m edges. The latter is almost linear due to the recent results of Sherman [23] and Kelner et al. [13].

OriginalspracheEnglisch
TitelProceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Herausgeber (Verlag)Association for Computing Machinery
Seiten227-238
Seitenumfang12
ISBN (Print)9781611973389
DOIs
PublikationsstatusVeröffentlicht - 2014
Veranstaltung25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, USA/Vereinigte Staaten
Dauer: 5 Jan. 20147 Jan. 2014

Publikationsreihe

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Konferenz

Konferenz25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Land/GebietUSA/Vereinigte Staaten
OrtPortland, OR
Zeitraum5/01/147/01/14

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