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GEOENGINE - Topology and Optimization

Topology and Optimization (3rd semester)
Instructor Dr.-Ing. S. Becker
Lecture Thursday / weekly 14:00 - 15:30
Start: 22-Oct-2015
Room: M2.370
Wednesday / biweekly 11:30 - 13:00
Start: 04-Nov-2015
Room: M2.370

Course Contents

Least-squares principle, Gauss-Markov-Model, adjustment phased with respect to observation, network design, quadratic (and linear) programming, Linear Complementarity Problem (LCP) with corresponding algorithms, basics in topology, incidence and adjacency, optimal routing and network analysis


Recommended textbooks
  • Meissl, P. (1982): Least Squares Adjustment – A Modern Approach.Mitteilungen der geodätischen Institute der technischen Universität Graz, Folge 43
  • Koch, K.R. (1997): Parameter Estimation and Hyphotesis Testing in linear Models. Springer, Berlin, 333p.
  • Grafarend, E.W., Sanso, F. (Ed.) (1985): Optimization and Design of Geodetic Networks. Springer, Berlin, 606p.
  • Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C. (2002): Introduction to Algorithms. The MIT Press, Cambridge, 1180p.


pdf icon  Lecture Notes:

  1. Introduction
  2. Basics of Topology
  3. Networks and Trees
  4. Optimization Problems based on Networks and Trees
  5. Probabilistic Graphical Models
  6. Linear Programming for Optimization Problems
  7. Adjustment Problems


lecture from Title mark out
28-Oct-2015 Introduction and Basics of Topology PDF
29-Oct-2015 Topological Relationships and Graph Theory PDF
05-Nov-2015 Graph Theory and Traversal of Graphs PDF
12-Nov-2015 Traversal of Graphs and Trees PDF
19-Nov-2015 Traversal of Trees and Shortest Path Problem PDF
26-Nov-2015 Maximum Flow Problem PDF
03-Dec-2015 Assignment Problems PDF
10-Dec-2015 Map Coloring Problem PDF
16-Dec-2015 Probabilistic Graphical Models, Part 1 PDF
17-Dec-2015 Probabilistic Graphical Models, Part 2 PDF
14-Jan-2016 Total Least Squares PDF
21-Jan-2016 Linear Programming for Optimization Problems
28-Jan-2016 Design and Optimization of Geodetic Networks
First Order Design – Example
Second Order Design – Example
04-Feb-2016 Preparation for the Exam
exercises from Title mark out
04-Nov-2015 Eulerian and Hamiltonian Graphs PDF
18-Nov-2015 Graphs and Trees PDF
25-Nov-2015 Trees and Shortest Path Problem PDF
27-Jan-2015 Linear Programming PDF

pdf icon Exercise Sheets:

Former examinations