Algorithms to Separate {0,1/2}-Chvatal-Gomory Cuts

Chvatal-Gomory cuts are among the most well-known classes of cutting planes for general integer linear programs (ILPs). In case the constraint multipliers are either 0 or 1/2, such cuts are known as {0, 1/2}-cuts. It has been proven by Caprara and Fischetti (1996) that separation of {0, 1/2}-cuts is NP-hard. In this paper, we study … Read more

A new model and a computational study for Demand-wise Shared Protection

This report combines the contributions to INOC 2005 (Wessälly et al., 2005) and DRCN 2005 (Gruber et al., 2005). A new integer linear programming model for the end-to-end survivability concept deman d-wise shared protection (DSP) is presented. DSP is based on the idea that backup capacity is dedicated to a particular demand, but shared within … Read more

Linear Programming Lower Bounds for Minimum Converter Wavelength Assignment in Optical Networks

In this paper, we study the conflict-free assignment of wavelengths to lightpaths in an optical network with the opportunity to place wavelength converters. To benchmark heuristics for the problem, we develop integer programming formulations and study their properties. Moreover, we study the computational performance of the column generation algorithm for solving the linear relaxation of … Read more

Provably Good Solutions for Wavelength Assignment in Optical Networks

In this paper, we study the minimum converter wavelength assignment problem in optical networks. To benchmark the quality of solutions obtained by heuristics, we derive an integer programming formulation by generalizing the formulation of Mehrotra and Trick (1996) for the vertex coloring problem. To handle the exponential number of variables, we propose a column generation … Read more

Polyhedral investigations on stable multi-sets

Stable multi-sets are an evident generalization of the well-known stable sets. As integer programs, they constitute a general structure which allows for a wide applicability of the results. Moreover, the study of stable multi-sets provides new insights to well-known properties of stable sets. In this paper, we continue our investigations started in Koster and Zymolka … Read more

Transparent optical network design with sparse wavelength conversion

We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse … Read more

Stable Multi-Sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets. For the … Read more