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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: 20-Oct-2016
Room: M 2.370
Wednesday / biweekly 11:30 - 13:00
Start: 2-Nov-2016
Room: M 17.73

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
20-Oct-2016 Introduction and Basics of Topology PDF
27-Oct-2016 Topological Relationships and Graph Theory PDF
03-Nov-2016 Graph Theory and Traversal of Graphs PDF
17-Nov-2016 Traversal of Graphs and Trees PDF
24-Nov-2016 Traversal of Trees and Shortest Path Problem PDF
01-Dec-2016 Maximum Flow Problem PDF
08-Dec-2016 Assignment Problems PDF
15-Dec-2016 Map Coloring Problem PDF   PDF
22-Dec-2016 Probabilistic Graphical Models, part 1 PDF   PDF
12-Jan-2017 Probabilistic Graphical Models, part 2 PDF   PDF
19-Jan-2017 Probabilistic Graphical Models, part 3 PDF
19-Jan-2017 Linear Programming for Optimization Problems PDF
26-Jan-2017 Total Least Squares PDF
02-Feb-2017 Design and Optimization of Geodetic Networks PDF
09-Feb-2017 Preparation for the Exam PDF
exercises from Title mark out
02-Nov-2016 Eulerian and Hamiltonian Graphs PDF
23-Nov-2016 Graphs and Trees PDF
30-Nov-2016 Trees and Shortest Path Problem Quicktime
25-Jan-2017 Linear Programming Quicktime
02-Feb-2017 First Order Design Problem Quicktime
02-Feb-2017 Second Order Design Problem Quicktime

pdf icon Exercise Sheets:


Former examinations