Graph Algorithms

In the winter semester 2021/2022, I teach the course on Graph Algorithms. The lecture covers advanced algorithms for shortest paths, network flows, minimum spanning trees, and some other graph problems. Several graph data structures will be mentioned, too.

The course is scheduled on Wednesdays from 10:40 in room S322 and taught in English this year.

If you want to consult anything, please write an e-mail to mares@kam.mff.cuni.cz and we will discuss possibilities.

date topics
6. 10. Network flows: formulation of the problem, basic theorems (min-cut/max-flow, integrality), Ford-Fulkerson algorithm. Applications to bipartite matchings and disjoint paths.
13. 10. Network flows: Dinitz algorithm and its behavior on special networks. Scaling algorithm for integer capacities.
20. 10. Disjoint paths, cuts and separators using flows. Finding cuts probabilistically: the Karger-Stein algorithm.
27. 11. Plan: Shortest paths: general properties, woes with negative cycles, shortest path trees. Relaxation scheme and a proof of its correctness. Bellman-Ford-Moore algorithm as a special case of relaxation.

Recommended reading

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