Předmět Graph Algorithms (MA015)

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Materiál	Typ	Datum	Počet stažení

Cíl

At the end of the course students will under know and understand important graph algorithms beyond the reach of standard algorithms and data structures courses. Covered algorithms span most of the important application areas of graphs algorithms. The students also should be able to choose an algorithm best suited for a given task, modifying it when necessary, and estimate its complexity.

Osnova

Cover problems: vertex cover, dominating set, feedback vertex set, feedback arc set. Parameterized complexity of algorithms.Dynamic algorithms on tree-like structures: algorithms for trees, graphs of bounded tree-width, path-width, clique-width, oriented tree-like graphs.Graph isomorphism: trees, planar graphs, general-case heuristics (colour coding).Planar drawing and testing: path addition method, PQ/SPQR trees, Boyer-Myrwold algorithm.Network flows: Edmonds-Karp algorithm. Dinic's algorithm and its modifications (e.g. unit capacities, integer capacities). Three Indians algorithm. Minimum-cost flow algorithms.Shortest paths: A* algorithm, reach-based algorithms, hub labelling, hierarchical decompositions, distance oracles.Spanning trees: modifications of Borůvka's and Jarnik§s algorithm for particular input instances (e.g. planar graphs). Steiner trees.Cuts (non-flow based algorithms): Gomory-Hu trees, globally minimum cut, Nagamochi-Ibaraki algorithm, randomized algorithms (Karger-Stein).

Literatura

doporučená literaturaMAREŠ, Martin. Krajinou grafových algoritmů. Pracovní verze. : ITI, 2015. URL infoCORMEN, Thomas H., Charles E. LEISERSON a Ronald L. RIVEST. Introduction to algorithms. Cambridge: MIT Press, 1989. xvii, 1028. ISBN 0-07-013143-0. info

Požadavky

MB005 Základy matematiky ||( MB101 Lineární modely && MB102 Dif. a integrální počet )||( MB201 Lineární modely B && MB102 Dif. a integrální počet )||( MB101 Lineární modely && MB202 Dif. a integrální počet B )||( MB201 Lineární modely B && MB202 Dif. a integrální počet B )||( PřF:M1120 Diskrétní matematika )|| PROGRAM ( N - IN )|| PROGRAM ( N - AP )Knowledge of basic graph algorithms, to the extent covered by the course IV003 Algorithms and Data Structures II. Specifically, students should already understand the following algorithms:Graphs searching: DFS, BFS.Network flows: Ford-Fulkerson, Golderg (push-relabel).Minimum spanning trees: Boruvka, Jarnik (Prim), Kruskal.Shortest paths: Bellman-Ford, Dijkstra.

Garant

prof. RNDr. Mojmír Křetínský, CSc.

Vyučující

Mgr. Jan Obdržálek, PhD.Frédéric Dupont Dupuis, Ph.D.Mgr. Bc. Tomáš Janíkprof. RNDr. Petr Hliněný, Ph.D.