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Algorithms and networks Fall 2009

Algorithms and networks Fall 2009. Today. Graphs and networks and algorithms: what and why? This course: organization Case introduction: facility location problems Shortest path I. What and why?. Started in 1736 with paper by Euler: bridges of Königsberg

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Algorithms and networks Fall 2009

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  1. Algorithms and networksFall 2009

  2. Today • Graphs and networks and algorithms: what and why? • This course: organization • Case introduction: facility location problems • Shortest path I

  3. What and why?

  4. Started in 1736 with paper by Euler: bridges of Königsberg Can we make a walk where we cross each bridge once (Euler-tour)? Graphs

  5. Networks • Graphs are a model for many things in the real world: • Road networks, electrical networks, organizational diagrams, social networks, structure of software, data bases, … • Often with additional information: network is graph with some extra info (like weights, lengths, labels, …)

  6. Problems • Often, we want to compute something on the network, motivated from the application (or theoretical curiosity). • How good and fast can we let the computer do this computation?

  7. Algorithms and complexity • Algorithms • Exact, heuristic, special case • Polynomial time, exponential time, … • … • Complexity • NP-completeness, other classes • …

  8. Techniques • Combinatorial algorithms • Branch and bound • Local search (iterative improvement, simulated annealing, tabu search, …) • (Integer) linear programming • …

  9. Model and algorithm • Real life problem • Mathematical model of real life problem • Algorithm for mathematical model • Solution produced by algorithm • Translation of solution to solution for real life problem

  10. This course (organization)

  11. Teacher 1 • Marinus Veldhorst • marinus@cs.uu.nl • 030-2534450 • CGN office A310

  12. Teacher 2 • Hans Bodlaender • hansb@cs.uu.nl • 030-2534409 • Kamer A302 CGN

  13. Algorithms and networks • 2 times per week lectures • 8 sets of exercises • Two weeks time for handing in • 2 partial exams

  14. Final grade • (Average exercise sets *2 + 1e exam + 2e exam)/4 • Assuming • Exercise sets at least 6 • Average exams at least 5

  15. Exercise sets • 8 sets • Grade • Hand in on paper, before or on deadline • Dutch or English • Write clear, legible, etc. • Unreadable, messy: 0

  16. Purpose of course • Knowing and being able to use and apply • Important algorithmic techniques • Important algorithms • Modelling • In particular for combinatorial problems involving graphs and networks

  17. Topics • Algorithms • Modeling, principles (PTAS, NP-completeness) • Graph and Network algorithms • Paths (shortest paths, TSP) • Flow (max flow, min cost flow) • Matching (and stable marriage) • Trees (finding Steiner tree, exploiting treewidth,…) • Small world graphs (six degrees of separation) • Facility location (dominating set problem) • Mobile communication (algorithms for unit disk graphs, frequency assignment problem)

  18. The website of this course • See www.cs.uu.nl/docs/vakken/an for • Powerpoint files • Exercises • Schedules • Dates, etc

  19. Studying this course • Be there! • Materials are scattered literature: often hard to study at home if you were not at the course • If you are not at the course: borrow/copy notes of other students! • Make notes • Do your exercises • Preferably before the corresponding exam, even when the deadline is later! • Use the powerpoints and pdf’s

  20. Exercises • Hand-in on paper • Use folder • Once during course you can extend your deadline with three days (joker-rule)

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