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pro vyhledávání: '"Au, Yu Hin"'
Autor:
Au, Yu Hin, Tunçel, Levent
We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lov\'{a}sz--Schrijver SDP operator $\text{LS}_+$, with a particular focus on finding and characterizing the smallest graphs with a given $\text{LS}_+$-rank (
Externí odkaz:
http://arxiv.org/abs/2401.01476
Autor:
Au, Yu Hin, Tunçel, Levent
We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lov\'asz-Schrijver SDP operator $\text{LS}_+$. In particular, we focus on a search for relatively small graphs with high $\text{LS}_+$-rank (i.e., the least
Externí odkaz:
http://arxiv.org/abs/2303.08971
Autor:
Au, Yu Hin
Let $s_d(n)$ be the number of distinct decompositions of the $d$-dimensional hypercube with $n$ rectangular regions that can be obtained via a sequence of splitting operations. We prove that the generating series $y = \sum_{n \geq 1} s_d(n)x^n$ satis
Externí odkaz:
http://arxiv.org/abs/2205.03680
We explore some connections between association schemes and the analyses of the semidefinite programming (SDP) based convex relaxations of combinatorial optimization problems in the Lov\'{a}sz--Schrijver lift-and-project hierarchy. Our analysis of th
Externí odkaz:
http://arxiv.org/abs/2008.08628
Autor:
Au, Yu Hin
Publikováno v:
Journal of Integer Sequences 24 (2021) Article 21.1.1
The $n^{\text{th}}$ small Schr\"oder number is $s(n) = \sum_{k \geq 0} s(n,k)$, where $s(n,k)$ denotes the number of plane rooted trees with $n$ leaves and $k$ internal nodes that each has at least two children. In this manuscript, we focus on the we
Externí odkaz:
http://arxiv.org/abs/1912.00555
Publikováno v:
Journal of Integer Sequences 23 (2020) Article 20.1.4
We study a two-parameter generalization of the Catalan numbers: $C_{d,p}(n)$ is the number of ways to subdivide the $d$-dimensional hypercube into $n$ rectangular blocks using orthogonal partitions of fixed arity $p$. Bremner \& Dotsenko introduced $
Externí odkaz:
http://arxiv.org/abs/1903.00813
Akademický článek
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Autor:
Au, Yu Hin, Tunçel, Levent
Publikováno v:
Discrete Optimization 27 (2018), 103-129
We consider operators acting on convex subsets of the unit hypercube. These operators are used in constructing convex relaxations of combinatorial optimization problems presented as a 0,1 integer programming problem or a 0,1 polynomial optimization p
Externí odkaz:
http://arxiv.org/abs/1608.07647
Autor:
Au, Yu Hin Jay
In this thesis, we study the behaviour of Lovasz and Schrijver's lift-and-project operators N and N_0 while being applied recursively to the fractional stable set polytope of a graph. We focus on two related conjectures proposed by Liptak and Tuncel:
Externí odkaz:
http://hdl.handle.net/10012/3485
Autor:
Au, Yu Hin, Tunçel, Levent
Publikováno v:
SIAM Journal on Discrete Mathematics 30(1) (2016), 411-451
We consider lift-and-project methods for combinatorial optimization problems and focus mostly on those lift-and-project methods which generate polyhedral relaxations of the convex hull of integer solutions. We introduce many new variants of Sherali--
Externí odkaz:
http://arxiv.org/abs/1312.5972