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Unformatted text preview: Summary of what you have learned up to Prelim 1 (ENGRI 115, Fall 2007) What is Operations Research? Real world problem (application) → Model → Algorithm → Validation. Graph definitions • Graph, nodes (vertices), edges (arcs). Undirected graph, directed graph. Simple graph (no loops or multiple edges). • Subgraph, spanning subgraph. • Connected graph, components of a graph. • Path, directed path, cycle, directed cycle, acyclic graph (forest), acyclic directed graph, tree, spanning tree, leaves. • Costs on edges. Cost of a path, cost of a tree. • Flow, value of flow. Capacities on arcs. Cut, capacity of a cut. The Minimum Spanning Tree Problem • Applications: Communication/Power network between geographical locations; Compact Data Storage. • Model: Undirected graph represents the network, assign costs to edges, find spanning tree that has minimal total cost . • Algorithms: Prim’s Algorithm , Kruskal’s (Greedy) Algorithm , Reverse Greedy Algorithm , Decrementing Edge Algorithm (start with spanning tree and look for improving edges)....
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- Fall '05
- Graph Theory, Critical path method, Dijkstra