Adrian Zymolka

Demand-wise shared protection for meshed optical networks

In this paper, a new shared protection mechanism for meshed optical networks is presented. Significant network design cost reductions can be achieved in comparison to the well-known 1+1 protection scheme. Demand-wise Shared Protection (DSP) is based on the diversification of demand routings and exploits the network connectivity to restrict the number of backup lightpaths needed to provide the desired level of protection. Computational experiments illustrate the benefits of the DSP concept for cost efficient optical network designs.

A computational study for demand-wise shared protection

In this paper, we compare the new resilience mechanism demand-wise shared protection (DSP) with dedicated and shared path protection. The computational study on five realistic network planning scenarios reveals that that the best solutions for DSP are on average 15% percent better than the corresponding 1+1 dedicated path protection solutions, and only 15% percent worse than shared path protection.

Stable multi-sets

Abstract. 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 stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined. The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks.

On cycles and the stable multi-set polytope

Stable multi-sets are an integer extension of stable sets in graphs. In this paper, we continue our investigations started by Koster and Zymolka [Stable multi-sets, Math. Methods Oper. Res. 56(1) (2002) 45-65]. We present further results on the stable multi-set polytope and discuss their computational impact. The polyhedral investigations focus on the cycle inequalities. We strengthen their facet characterization and show that chords need not weaken the cycle inequality strength in the multi-set case. This also helps to derive a valid right hand side for clique inequalities. The practical importance of the cycle inequalities is evaluated in a computational study. For this, we revisit existing polynomial time separation algorithms. The results show that the performance of state-of-the-art integer programming solvers can be improved by exploiting this general structure. ructure.