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Algorithms and Networks: Exploring Graphs and Optimization Techniques

This course delves into algorithms and networks, focusing on graph theory and its real-world applications. Topics include shortest paths, flow algorithms, matching problems, and combinatorial algorithms. Students will explore the complexities of algorithms, including NP-completeness, and apply important techniques such as heuristic methods and linear programming. Regular lectures and exercise sets reinforce learning, while examinations assess understanding. Developed by Marinus Veldhorst and Hans Bodlaender, the course aims to equip students with the skills to model and solve practical problems using algorithmic techniques.

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Algorithms and Networks: Exploring Graphs and Optimization Techniques

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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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