Network planning has come to great importance during the past decades. Today's telecommunication, traffic systems, and logistics would not have been evolved to the current state without careful analysis of the underlying network problems and precise implementation of the results obtained from those examinations. Graphs with node and arc attributes are a very useful tool to model realistic applications, while on the other hand they are well understood in theory. We investigate network design problems which are motivated particularly from applications in communication networks and logistics. Those problems include the search for homogeneous subgraphs in edge labeled graphs where either the total number of labels or the reload cost are subject to optimize. Further, we investigate some variants of the dial a ride problem. On the other hand, we use node and edge upgrade models to deal with the fact that in many cases one prefers to change existing networks rather than implementing a newly computed solution from scratch. We investigate the construction of bottleneck constrained forests under a node upgrade model, as well as several flow cost problems under a edge based upgrade model. All problems are examined within a framework of multi-criteria optimization. Many of the problems can be shown to be NP-hard, with the consequence that, under the widely accepted assumption that P is not equal to NP, there cannot exist efficient algorithms for solving the problems. This motivates the development of approximation algorithms which compute near-optimal solutions with provable performance guarantee in polynomial time. / Netzplanung hat in den vergangenen Jahrzehnten an Bedeutung zugenommen. Der heutige Stand im Bereich von Telekommunikation, Verkehrsnetzen und in der Logistik wäre nicht in dem Maße erreicht worden, wenn nicht die zugrundeliegenden Netzplanungsprobleme sorgfältig analysiert und die daraus gewonnenen Erkenntnisse in die Realisierung eingeflossen wären. Für die Modellierung der durch die Praxis vorgegebenen Probleme erweisen sich Graphen mit Knoten- und Kantenbewertungen als gut geeignet, zumal diese Strukturen auch in der Theorie bereits gut untersucht sind. Wir betrachten Netzwerk-Design-Probleme aus dem Bereich der Planung von Kommunikations- und Logistiknetzwerken. Gegenstand ist zunächst die Suche nach homogenen Teilgraphen in Graphen mit Kantenlabels, wobei einerseits die Gesamtszahl der benutzten Labels minimiert wird, andererseits die Kosten unter einem Umladekosten-Modell optimiert werden. Weiter werden einige Varianten des Dial-A-Ride-Problems untersucht. Im zweiten Teil der Arbeit werden Netzwerk-Ausbau-Probleme betrachtet. Dies trägt der Tatsache Rechung, dass in vielen praktischen Fällen nur die Abänderung bestehender Netze und nicht die Neukonstruktion von Netzen in Frage kommt. Alle Probleme werden im Rahmen der Mehrkriterien-Optimierung betrachtet. Viele der betrachteten Probleme lassen sich als NP-hart nachweisen. Dies hat zur Folge, dass es - unter der gängigen Annahme, dass P ungleich NP ist - keine effizienten Lösungsalgorithmen geben kann. Daher entwickeln wir Approximationsalgorithmen, die in Polynomialzeit Näherungslösungen mit beweisbarer Gütegarantie berechnen.

Graduation date: 1995

We present a constant-factor approximation algorithm for computing an embedding of the shortest path metric of an unweighted graph into a tree, that minimizes the multiplicative distortion.

The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function may then be computed as the optimal estimator with respect to this measure field. We give an efficient procedure for effecting both computations, and for the determination of the optimal number of components.

Neural networks can be looked as a kind of intruments which is able to learn. For making the fruitful results of neural networks' learning possess parctical applied value, the thesis makes use of linear regression technics to strengthen the extended capability of RBF neural networks. The thesis researches the training methods of RBF neural networks, and retains the frame of OLS(orthogonal least square) learning rules which is published by Chen and Billings in 1992. Besides, aiming at the RBF's characteristics, the thesis brings up improved learning rules in first and second phases, and uses " early stop" to be the condition of training ceasing. To sum up, chiefly the thesis applies some technics of statistic linear regression to strenthen the extended capability of RBF, and using different methods to do computer simulation in different noise situations.

Thesis Ph. D.--Applied mathematics--Åbo akademi, 2005. / Bibliogr. p. 95-99.

Thèse de doctorat : Chimie. Chimie informatique et théorique : Strasbourg 1 : 2008. / Thèse soutenue sur un ensemble de travaux. Titre provenant de l'écran-titre. Bibliogr. 6 p.

Thesis--Ph. D., University of Hong Kong. / Mimeographed.

Thesis--M. Phil., University of Hong Kong, 1980.

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