Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Filho, Fernando Mário de Oliveira"'
We show that the $k$-point bound of de Laat, Machado, Oliveira, and Vallentin, a hierarchy of upper bounds for the independence number of a topological packing graph derived from the Lasserre hierarchy, converges to the independence number.
Comm
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Externí odkaz:
http://arxiv.org/abs/2306.02725
Witsenhausen's problem asks for the maximum fraction $\alpha_n$ of the $n$-dimensional unit sphere that can be covered by a measurable set containing no pairs of orthogonal points. The best upper bounds for $\alpha_n$ are given by extensions of the L
Externí odkaz:
http://arxiv.org/abs/2304.05429
Publikováno v:
Combinatorica 43 (2023), no. 5, 909-938
The theta body of a graph, introduced by Gr\"otschel, Lov\'asz, and Schrijver in 1986, is a tractable relaxation of the independent-set polytope derived from the Lov\'asz theta number. In this paper, we recursively extend the theta body, and hence th
Externí odkaz:
http://arxiv.org/abs/2206.03929
Publikováno v:
Proc. AMS 150 (2022), 3307-3322
We recursively extend the Lov\'asz theta number to geometric hypergraphs on the unit sphere and on Euclidean space, obtaining an upper bound for the independence ratio of these hypergraphs. As an application we reprove a result in Euclidean Ramsey th
Externí odkaz:
http://arxiv.org/abs/2106.09360
The average kissing number of $\mathbb{R}^n$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $\mathbb{R}^n$. We provide an upper bound for the average kissing number based on semidefinite
Externí odkaz:
http://arxiv.org/abs/2003.11832
Autor:
de Laat, David, Machado, Fabrício Caluza, Filho, Fernando Mário de Oliveira, Vallentin, Frank
Publikováno v:
Mathematical Programming 194 (2022), 533-567
We give a hierarchy of $k$-point bounds extending the Delsarte-Goethals-Seidel linear programming $2$-point bound and the Bachoc-Vallentin semidefinite programming $3$-point bound for spherical codes. An optimized implementation of this hierarchy all
Externí odkaz:
http://arxiv.org/abs/1812.06045
Publikováno v:
Mathematika 65 (2019) 785-787
For $n \geq 2$ we construct a measurable subset of the unit ball in $\mathbb{R}^n$ that does not contain pairs of points at distance 1 and whose volume is greater than $(1/2)^n$ times the volume of the ball. This disproves a conjecture of Larman and
Externí odkaz:
http://arxiv.org/abs/1808.07299
Publikováno v:
Discrete Analysis, 2020:10
We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each $n \geq 2$ we present a convex optimization problem whose optimal value is the largest possible ratio
Externí odkaz:
http://arxiv.org/abs/1808.02346
Publikováno v:
Math. Program. 191 (2022), 487-558
We introduce the cone of completely-positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequen
Externí odkaz:
http://arxiv.org/abs/1804.09099
The kissing number of $\mathbb{R}^n$ is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. Mittelmann and Vallentin (2010), based on the semidefinite programming bound of Bachoc and Vallent
Externí odkaz:
http://arxiv.org/abs/1609.05167