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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Chan, T.-H.H. Chang, K.L. Raman, R. |
| Copyright Year | 2009 |
| Description | Author affiliation: Max-Planck-Institut für Informatikm 66123 Saarbrücken, Germany (Chan, T.-H.H.; Raman, R.) || Yahoo Labs, Santa Clara, California, USA (Chang, K.L.) |
| Abstract | The Lovász ϑ-function [Lov79] on a graph G = (V,E) can be defined as the maximum of the sum of the entries of a positive semidefinite matrix X, whose trace Tr(X) equals 1, and Xij = 0 whenever {i, j} ∈ E. This function appears as a subroutine for many algorithms for graph problems such as maximum independent set and maximum clique. We apply Arora and Kale's primal-dual method for SDP to design an approximate algorithm for the ϑ-function with an additive error of δ ≫ 0, which runs in time $O(α^{2}n^{2}/δ^{2}$ log n · Me), where α = ϑ(G) and Me = $O(n^{3})$ is the time for a matrix exponentiation operation. Moreover, our techniques generalize to the weighted Lovász ϑ-function, and both the maximum independent set weight and the maximum clique weight for vertex weighted perfect graphs can be approximated within a factor of (1+∊) in time $O(∊^{−2}n^{5}$ log n). |
| Starting Page | 2808 |
| Ending Page | 2812 |
| File Size | 804788 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781424443123 |
| DOI | 10.1109/ISIT.2009.5205779 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2009-06-28 |
| Publisher Place | South Korea |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Approximation algorithms Polynomials Algorithm design and analysis Size measurement Time measurement Performance evaluation Graph theory Ellipsoids |
| Content Type | Text |
| Resource Type | Article |
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