This paper presents a new method and a constraint-based objective function to solve two problemsrelated to the design of optical telecommunication networks, namely the Synchronous Optical Net-work Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network DesignProblem (IDP). These network topology problems can be represented as a graph partitioning withcapacity constraints as shown in previous works. We present here a new objective function and anew local search algorithm to solve these problems. Experiments conducted in C
A special case of the IDP problem where all the edges have the same weight, is studied in @cite_1 . This special case is called the problem. Given a simple undirected graph @math and a value @math , we want to find a partitioning of @math , @math such that @math . The authors present two linear-time-approximation algorithms with fixed performance guarantee.
@cite_1
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A feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomial-time algorithms are provided for approximating the problem of finding a feedback vertex set of G with smallest weight. When the weights of all vertices in G are equal, the performance ratio attained by these algorithms is 4-(2 n). This improves a previous algorithm which achieved an approximation factor of @math for this case. For general vertex weights, the performance ratio becomes @math where @math denotes the maximum degree in G. For the special case of planar graphs this ratio is reduced to 10. An interesting special case of weighted graphs where a performance ratio of 4-(2 n) is achieved is the one where a prescribed subset of the vertices, so-called blackout vertices, is not allowed to participate in any feedback vertex set. It is shown how these algorithms can improve the search performance for constraint satisfaction problems. An application in the area of Bayesian inference of graphs with blackout vertices is also presented.