We introduce the ratio-cut polytope defined as the convex hull of ratio-cut vectors
corresponding to all partitions of n points in R^m into at most K clusters. This polytope is …

Hub location problems can be modeled in several ways, one of which is the path-based
family of models that make use of four-index variables. Clique inequalities are frequently …

The stable set problem is a fundamental combinatorial optimisation problem, that is known
to be very difficult in both theory and practice. Some of the solution algorithms in the …

In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation
for K-means clustering. In this paper, we further investigate both theoretical and …

We discuss minimum weight clustered dominating trees that find applications in the wireless
sensor network design based on a clustered independent set structure. A cluster consists of …

The Lov\'asz theta function $\theta (G) $ provides a very good upper bound on the stability
number of a graph $ G $. It can be computed in polynomial time by solving a semidefinite …

In the context of the maximum stable set problem, rank inequalities impose that the
cardinality of any set of vertices contained in a stable set be, at most, as large as the stability …

Cutting planes have been an important factor in the impressive progress made by integer
programming (IP) solvers in the past two decades. However, cutting planes have had little …

Boolean functions have a fundamental role in neural networks and machine learning.
Enumerating these functions and significant subclasses is a highly complex problem …

The Lovász theta function θ (G) provides a very good upper bound on the stability number of
a graph G. It can be computed in polynomial time by solving a semidefinite program (SDP) …