Cuts and metrics are well-known objects that arise-independently, but with many deep and
fascinating connections-in diverse fields: in graph theory, combinatorial optimization …

Given a set of entities, Cluster Analysis aims at finding subsets, called clusters, which are
homogeneous and/or well separated. As many types of clustering and criteria for …

We study unconstrained quadratic zero–one programming problems having n variables from
a polyhedral point of view by considering the Boolean quadric polytope QP n in n (n+ 1)/2 …

In this paper we consider a clustering problem that arises in qualitative data analysis. This
problem can be transformed to a combinatorial optimization problem, the clique partitioning …

In this paper we describe several forms of the k-partition problem and give integer
programming formulations of each case. The dimension of the associated polytopes and …

The corridor allocation problem (CAP) seeks an arrangement of facilities along a central
corridor defined by two horizontal lines parallel to the x-axis of a Cartesian coordinate …

This book offers a self-contained introduction to the field of semidefinite programming, its
applications in combinatorial optimization, and its computational methods. We equip the …

While graph covering is a fundamental and well-studied problem, this field lacks a broad
and unified literature review. The holistic overview of graph covering given in this article …

We describe a decomposition framework and a column generation scheme for solving a min-
cut clustering problem. The subproblem to generate additional columns is itself an NP-hard …

Given the integer polyhedron P t:= conv {x∈ ℤ n: Ax⩽ b}, where A∈ ℤ m× n and b∈ ℤ m, a
Chvátal-Gomory (CG) cut is a valid inequality for P 1 of the type λτ Ax⩽⌊ λτ b⌋ for some λ∈ …