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Abstract: Let vc(G) denote the minimum size of a vertex cover of a graph G = (V; E). It is well-known that one can approximate vc(G) to within a factor of 2 in polynomial time; and despite considerable investigation, no (2 \Gamma ") approximation algorithm has been found for any " ? 0. Because of the many connections between the independence number ff(G) and the Lov'asz theta function #(G), and because vc(G) = jV j \Gamma ff(G), it is natural to ask how well jV j \Gamma #(G) approximates vc(G). It is... (Update)
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...is equivalent to the Lovasz theta problem. We briefly mention this relaxation below. This equivalence was established in Kleinberg and Goemans [34]. Also refer to Benson and Ye [6] for more details. The maximum stable set problem is max # # # # # # # # # 0.5 . 0 0.25 ....
...M and distributes the computations among the processors evenly. These conditions are not as well satisfied for the Lovasz # problem [18]. Given an undirected graph G = V, E) the Lovasz number is the optimal objective value to the semidefinite program maximize 1 . X...
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9: Geometric Algorithms and Combinatorial Optimization (context) - Grotschel, Lov'asz et al. - 1993
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7: Johnson D.: Approximation algorithms for combinatorial problems. Jour. of Computer and Syst. Sci., 1974, 9, 256-278.
BibTeX entry: (Update)
J. Kleinberg and M.X. Goemans, The Lov'asz theta function and a semidefinite programming relaxation of vertex cover, SIAM J. Discr. Math. Vol. 11: 196--204, 1997. http://citeseer.ist.psu.edu/kleinberg95lovasz.html More
@article{ kleinberg98lovasz,
author = "Jon M. Kleinberg and Michel X. Goemans",
title = "The Lovasz Theta Function and a Semidefinite Programming Relaxation of Vertex Cover",
journal = "SIAM Journal on Discrete Mathematics",
volume = "11",
number = "2",
pages = "196-204",
year = "1998",
url = "citeseer.ist.psu.edu/kleinberg95lovasz.html" }
Citations (may not include all citations):415 Improved approximation algorithms for maximum cut and satisf.. - Goemans, Williamson - 1994
99 Approximate graph coloring by semidefinite programming - Karger, Motwani et al. - 1994
75 Approximation algorithms for set covering and vertex cover p.. (context) - Hochbaum - 1982
52 A local-ratio theorem for approximating the weighted vertex .. (context) - Bar-Yehuda, Even - 1985
34 Ramsey numbers and an approximation algorithm for the vertex.. (context) - Monien, Speckenmeyer - 1985
23 Approximating the independence number via the `- function (context) - Alon, Kahale
13 Forbidden intersections (context) - Frankl, Rodl - 1987
10 A counterexample to Borsuk's Conjecture (context) - Kahn, Kalai - 1993
9 A comparison of the Delsarte and Lov'asz bounds (context) - Schrijver - 1979
5 Self-dual polytopes and the chromatic number of distance gra.. (context) - Lov'asz - 1983
3 Randomized graph products, chromatic numbers, and the Lov'as.. - Feige - 1995
3 Drei Satze uber die n-dimensionale euklidische Sphare (context) - Borsuk - 1933
1 the Shannon capcity of a graph (context) - Lov'asz - 1979
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