Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs G where the stable set polytope STAB(G) coincides with the clique constraint stable set polytope QSTAB(G). For all imperfect graphs STAB(G) \subset QSTAB(G) holds and, therefore, it is … Read more
The task of scheduling communications between satellites and ground control stations is getting more and more critical since an increasing number of satellites must be controlled by a small set of stations. In such a congested scenario, the current practice, in which experts build hand-made schedules, often leaves a large number of communication requests unserved. … Read more
While dealing with uncertainty in linear programs, the robust optimization framework proposed by Bertsimas and Sim appears as relevant. In particular, it can readily be extended for integer linear programming. This paper outlines the polyhedral impacts of this robust model for the 0-1 knapsack problem. It shows especially how the classical cover cuts can be … Read more
We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal sub ject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain … Read more
One of perspective ways to exploit sparsity in the dependency graph of an optimization problem as J.N. Hooker stressed is nonserial dynamic programming (NSDP) which allows to compute solution in stages, each of them uses results from previous stages. The class of discrete optimization problems with the block-tree-structure matrix of constraints is considered. Nonserial dynamic … Read more
Chance-constrained programming is a relevant model for many concrete problems. However, it is known to be very hard to tackle directly. In this paper, the chance-constrained knapsack problem (CKP) is addressed. Relying on the recent advances in robust optimization, a tractable combinatorial algorithm is proposed to solve CKP. It always provides feasible solutions for CKP. … Read more
We consider a knapsack problem with precedence constraints imposed on pairs of items, known as the precedence constrained knapsack problem (PCKP). This problem has applications in management and machine scheduling, and also appears as a subproblem in decomposition techniques for network design and other related problems. We present a new approach for determining facets of … Read more
The polyhedral homotopy method, which has been known as a powerful numerical method for computing all isolated zeros of a polynomial system, requires all mixed cells of the support of the system to construct a family of homotopy functions. Finding the mixed cells is formulated in terms of a linear inequality system with an additional … Read more
We consider the problem of interconnecting a set of customer sites using SONET rings of equal capacity, which can be defined as follows: Given an undirected graph G=(V,E) with nonnegative edge weight d(u,v), (u,v) in E, and two integers K and B, find a partition of the nodes of G into K subsets so that … Read more
In Multi-Input Multi-Output (MIMO) systems, Maximum-Likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on Semi-Definite Programming (SDP). We introduce several SDP relaxation models for MIMO systems, with … Read more