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The roommate problem with externalities
(Springer, 2020)
This paper extends the roommate problem to include externalities, allowing preferences for a partner to depend on the situation of others. Stability concepts for matchings and partitions of the set of agents are proposed ...
A polyhedral study of the maximum stable set problem with weights on vertex-subsets
(Elsevier Science, 2016-09)
Given a graph G = (V, E), a family of nonempty vertex-subsets S ⊆ 2 V , and a weight w : S → R+, the maximum stable set problem with weights on vertex-subsets consists in finding a stable set I of G maximizing the sum of ...
Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
(Elsevier Science, 2014-02)
We study Lovász and Schrijver's hierarchy of relaxations based on positive semidefiniteness constraints derived from the fractional stable set polytope. We show that there are graphs G for which a single application of the ...
The problems of construction of the reachable sets for stable oscillatory systems and its applications
(2020-08)
“Reachable sets play a fundamental role in the theories of robust stability and the optimal control. The analysis of reachable sets gives a possibility to solve a wide class of problems related to the study of dynamic ...
Lift-and-project ranks of the stable set polytope of joined a-perfect graphs
(Elsevier Science, 2016-09)
In this paper we study lift-and-project polyhedral operators defined by Lovász and Schrijver and Balas, Ceria and Cornuéjols on the clique relaxation of the stable set polytope of webs. We compute the disjunctive rank of ...
Lovász–Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs
(Springer, 2017-03)
We study the Lovász–Schrijver lift-and-project operator (LS +) based on the cone of symmetric, positive semidefinite matrices, applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial ...
Nondegeneracy and stability in the limit of a one-phase singular perturbation problem
(Amer. Inst. Mathematical Sciences-AIMS, 2023)
We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the ...
Cross-identification of stellar catalogs with multiple stars: Complexity and Resolution
(Elsevier, 2018-08)
In this work, I present an optimization problem which consists of assigning entries of a stellar catalog to multiple entries of another stellar catalog such that the probability of such assignment is maximum. I show a way ...
On the facets of the lift-and-project relaxations of graph subdivisions
(Elsevier, 2011-08)
We study the behavior of lift-and-project procedures for solving combinatorial optimization problems as described by Lovász and Schrijver (1991), in the context of the stable set problem on graphs. Following the work of ...