### $2kn-\left(\genfrac{}{}{0pt}{}{2k+1}{2}\right)$. A note on extremal combinatorics of cyclic split systems.

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In this article we study the realistic network topology of Synchronous Digital Hierarchy (SDH) networks. We describe how providers fulfill customer connectivity requirements. We show that SDH Network design reduces to the Non-Disjoint m-Ring-Star Problem (NDRSP). We first show that there is no two-index integer formulation for this problem. We then present a natural 3-index formulation for the NDRSP together with some classes of valid inequalities that are used as cutting planes in a Branch-and-Cut...

In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered sets is established. A connection is then made with dimension reduction in time-dependent dynamic programming via the notion of a bounding label, a function that bounds the state-transition cost functions. In this context, the computational burden is partitioned between a time-independent dynamic programming step carried out on the bounding label and a direct evaluation carried out on a subset of “real” valued...

In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered sets is established. A connection is then made with dimension reduction in time-dependent dynamic programming via the notion of a bounding label, a function that bounds the state-transition cost functions. In this context, the computational burden is partitioned between a time-independent dynamic programming step carried out on the bounding label and a direct evaluation carried out on a subset of “real"...

The Algorithm in this paper is designed to find the shortest path in a network given time-dependent cost functions. It has the following features: it is recursive; it takes place bath in a backward dynamic programming phase and in a forward evaluation phase; it does not need a time-grid such as in Cook and Halsey and Kostreva and Wiecek's "Algorithm One”; it requires only boundedness (above and below) of the cost functions; it reduces to backward multi-objective dynamic programming if there are...

In this paper, we consider a regulation problem of an urban transportation network. From a given timetable, we aim to find a new schedule of multiple vehicles after the detection of a disturbance at a given time. The main objective is to find a solution maximizing the level of service for all passengers. This problem was intensively studied with evolutionary approaches and multi-agent techniques, but without identifying its type before. In this paper, we formulate the problem as a classical one...

Many of today’s systems are characterized by a network structure and evaluation of alternatives is based on multiple criteria. Network systems contain both positive and negative feedbacks. In the paper, a hybrid procedure is proposed for operation in network environment. The procedure is based on a combination of DEMATEL, ANP, and PROMETHEE approaches. DEMATEL is a comprehensive method for building and analyzing a structural model involving causal relationships between complex factors. For the network...

This paper deals with the so called grouping problem which arises in telecommunication network optimization when transmission equipment with a certain hierarchy is used. It is shown how this problem is embedded in the complete scheme of network optimization and a general combinatorial model is developed to derive afterwards a solution procedure. The implementation of this procedure forms part of a software tool for the complete problem of transmission network planning. Some results deriving from...