This chapter surveys how semidefinite programming can be used for finding good
approximative solutions to hard combinatorial optimization problems. The chapter begins …

Publisher Summary Matching is pairing: dividing a collection of objects into pairs. Typically
the objective is to maximize total profit (or minimize cost), where the profit of each possible …

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 …

We study the problem of finding ground states of spin glasses with exterior magnetic field,
and the problem of minimizing the number of vias (holes on a printed circuit board, or …

The integer programming models known as set packing and set covering have a wide range
of applications, such as pattern recognition, plant location, and airline crew scheduling …

A promising approach to achieve computational supremacy over the classical von Neumann
architecture explores classical and quantum hardware as Ising machines. The minimisation …

We introduce and study an eigenvalue upper bound ϕ (G) on the maximum cut mc (G) of a
weighted graph. The function ϕ (G) has several interesting properties that resemble the …

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∈ …

PII: 0167-6377(83)90016-0 Page 1 Volume 2, Number 3 OPERATIONS RESEARCH
LETTERS August 1983 THE MAX-CUT PROBLEM ON GRAPHS NOT CONTRACTIBLE TO …

Given an undirected graph G=(V, E) and a weight function c: E→ R on the edge set of G, the
max-cut problem asks for the largest sum of the weights on the edges between the classes …