We consider semidefinite programs, where all the matrices defining the problem commute. We show that in this case the semidefinite program can be solved through an ordinary linear program. As an application, we consider the max-cut problem, where the underlying graph arises from an association...

We show that, in any undirected graph, splitting off can be performed while preserving all cuts of value at most 3/4 times the minimum value, and this is best possible. This generalizes a classical splitting-off result of Lovasz.

We consider the scheduling problem of minimizing the average wighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on time-indexed formulation, the other on a completion-time formulation. We show...

The location of facilities in order to provide service for customers is a well-studied problem in the operations research literature. In this paper, we establish strong connextions between fair cost allocations and linear programming relaxations for several variants of the facility location...