Why is maximum clique often easy in practice?
JL Walteros, A Buchanan - Operations Research, 2020 - pubsonline.informs.org
To this day, the maximum clique problem remains a computationally challenging problem.
Indeed, despite researchers' best efforts, there exist unsolved benchmark instances with …
Indeed, despite researchers' best efforts, there exist unsolved benchmark instances with …
On integrality in semidefinite programming for discrete optimization
F De Meijer, R Sotirov - SIAM Journal on Optimization, 2024 - SIAM
It is well known that by adding integrality constraints to the semidefinite programming (SDP)
relaxation of the max-cut problem, the resulting integer semidefinite program is an exact …
relaxation of the max-cut problem, the resulting integer semidefinite program is an exact …
[HTML][HTML] On the Lovász theta function and some variants
L Galli, AN Letchford - Discrete Optimization, 2017 - Elsevier
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 …
can be computed efficiently by solving a semidefinite program (SDP). Actually, one can …
Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting
This paper considers a generalization of the “max-cut-polytope” conv {\xx^ T ∣ x ∈ R^ n,\|
x_k|= 1\hbox for\1 ≤ k ≤ n\} conv xx T∣ x∈ R n,| xk|= 1 for 1≤ k≤ n in the space of real …
x_k|= 1\hbox for\1 ≤ k ≤ n\} conv xx T∣ x∈ R n,| xk|= 1 for 1≤ k≤ n in the space of real …
Simplified semidefinite and completely positive relaxations
F Lieder - Operations Research Letters, 2015 - Elsevier
This paper is concerned with completely positive and semidefinite relaxations of quadratic
programs with linear constraints and binary variables as presented by Burer. It observes that …
programs with linear constraints and binary variables as presented by Burer. It observes that …