Vertex Sparsification and Oblivious Reductions
Name
Moitra-2013-VERTEX SPARSIFICATIO.pdf
Size
299.92 KB
Format
Adobe PDF
Checksum (MD5)
0b8d7d7fd8a9b5259c4909c2f2030b91
Author(s)
Moitra, Ankur
Date Issued
January 2013
Journal
SIAM Journal on Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Moitra, Ankur. “Vertex Sparsification and Oblivious Reductions.” SIAM Journal on Computing 42, no. 6 (January 2013): 2400–2423. © 2013, Society for Industrial and Applied Mathematics.
Version
Final published version
Abstract
Given an undirected, capacitated graph $G = (V, E)$ and a set $K \subset V$ of terminals of size $k$, we construct an undirected, capacitated graph $G' = (K, E')$ for which the cut function approximates the value of every minimum cut separating any subset $U$ of terminals from the remaining terminals $K - U$. We refer to this graph $G'$ as a cut-sparsifier, and we prove that there are cut-sparsifiers that can approximate all these minimum cuts in $G$ to within an approximation factor that depends only polylogarithmically on $k$, the number of terminals. We prove such cut-sparsifiers exist through a zero-sum game, and we construct such sparsifiers through oblivious routing guarantees. These results allow us to derive a more general theory of Steiner cut and flow problems, and allow us to obtain approximation algorithms with guarantees independent of the size of the graph for a number of graph partitioning, graph layout, and multicommodity flow problems for which such guarantees were previously unknown.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/100787337
