CSE5311M3 - Module 3 - Graph Algorithms This week Graph...

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1 Module 3 - Graph Algorithms This week Graph terminology Stacks and Queues Breadth-first-search Depth-first-search Connected Components Analysis of BFS and DFS Algorithms 8/30/2009 M KUMAR CSE5311 1 Please see Reference Books Course Syllabus Review of Asymptotic Analysis and Growth of Functions, Recurrences Sorting Algorithms Graphs and Graph Algorithms. Greedy Algorithms: Minimum spanning tree,Union-Find algorithms, Kruskal's Algorithm, Clustering, Huffman Codes, and Multiphase greedy algorithms. Dynamic Programming: Shortest paths, negative cycles, matrix chain multiplications, sequence alignment, RNA secondary structure, application examples. •N e t w o r k F l o w : Maximum flow problem, Ford-Fulkerson algorithm, augmenting paths, Bipartite matching problem, disjoint paths and application problems . 8/30/2009 M KUMAR CSE5311 2 NP and Computational tractability: Polynomial time reductions; The Satisfiability problem; NP-Complete problems; and Extending limits of tractability. Approximation Algorithms, Local Search and Randomized Algorithms
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2 Graph Preliminaries Examples of modeling by Graphs Darwin Adelaide Brisbane Sydney Melbourne Perth Module 1 Module3 Module 2 Module 4 Module 5 Module 6 Module 7 8/30/2009 M KUMAR CSE5311 3 Graph Terminologies A Graph consists of a set 'V' of vertices (or nodes) and a set 'E' of edges (or links). A graph can be directed or undirected. Edges in a directed graph are ordered pairs. The order between the two vertices is important. Example: (S,P) is an ordered pair because the edge starts at S and terminates at P. The edge is unidirectional Ed di t d h f dd i 8/30/2009 M KUMAR CSE5311 4 Edges of an undirected graph form unordered pairs. A multigraph is a graph with possibly several edges between thesamepairofvertices. Graphs that are not multigraphs are called simple graphs.
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3 Graph Terminologies (Contd) P S D A Q R T E 8/30/2009 M KUMAR CSE5311 5 G1: Undirected Graph G2: Directed Graph B C Graph Terminologies The degree d ( v ) of a vertex v is the number of edges incident to v . d (A) = three, d (D) = two In directed graphs indegree is the numbe o incoming In directed graphs, the number of incoming edges at the vertex and outdegree is the number of outgoing edges from the vertex. The indegree of P is 2, its outdegree is 1. The indegree of Q is 1, its outdegree is 1. P S 8/30/2009 M KUMAR CSE5311 6 D B A E C Q R T
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4 Paths and Cycles A path from vertex v 1 to v k is a sequence of vertices v 1 ,v 2 ,…,v k that are connected by edges (v 1 ,v 2 ), (v 2 ,v 3 ), …, (v k-1 ,v k ). Path from D to E (DABE D B A E C Path from D to E: (D,A,B,E) Edges in the path: (D,A), (A,B), (B,E) A path is simple if each vertex in it appears only once. DABE is a simple path.
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CSE5311M3 - Module 3 - Graph Algorithms This week Graph...

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