Lovász theta type norms and operator systems
نویسندگان
چکیده
منابع مشابه
On Minrank and the Lovász Theta Function
Two classical upper bounds on the Shannon capacity of graphs are the θ-function due to Lovász and the minrank parameter due to Haemers. We provide several explicit constructions of n-vertex graphs with a constant θ-function and minrank at least n for a constant δ > 0 (over various prime order fields). This implies a limitation on the θ-function-based algorithmic approach to approximating the mi...
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The Lovász theta function of a graph is a well-known upper bound on the stability number. It can be computed efficiently by solving a semidefinite program (SDP). Actually, one can solve either of two SDPs, one due to Lovász and the other to Grötschel et al. The former SDP is often thought to be preferable computationally, since it has fewer variables and constraints. We derive some new results ...
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In previous works an upper bound on the stability number (G) of a graph G based on convex quadratic programming was introduced and several of its properties were established. The aim of this investigation is to relate theoretically this bound (usually represented by (G)) with the well known Lovász #(G) number. To begin with, a new set of convex quadratic bounds on (G) that generalize and improv...
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Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1. real linear operators from Lp(μ1) to Lq(μ2), 1 ≤ p ≤ q ≤ ∞; 2. real linear operators between inner product spaces; 3. nonnegative linear operators acting between complexi...
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A recently introduced dualization technique for binary linear programs with equality constraints, essentially due to Poljak et al. [13], and further developed in Lemaréchal and Oustry [9], leads to simple alternative derivations of well-known, important relaxations to two well-known problems of discrete optimization: the maximum stable set problem and the maximum vertex cover problem. The resul...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.03.022