nlec1 - Outline and References Introduction Minimum...

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Outline and References Introduction Networks*: Lecture 1 Minimum Spanning Tree (MST) Chinese Postman Problem (CPP) Skim Sections 6.1 and 6.2, read Amedeo R. Odoni Sections 6.3- 6.4.4 in Larson and Odoni November 15, 2004 Far more detailed coverage in Ahuja, R., T. L. Magnanti and J. B. Orlin, * Thanks to Prof. R. C. Larson for Network Flows, Prentice-Hall, 1993. some of the slides A B C D E Nodes B and D Directed Arc Undirected Arc Towns Cities Electrical junctions Arcs/ Edges/ Links Circuit components Project tasks Network with Terminology Examples of Nodes & Arcs Nodes/ Vertices/ Points Street intersections Project milestones Street segments Country roads Airplane travel time

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Network Terminology Network Terminology - con't. N = sets of nodes In-degree Tree of an Spanning tree of A = set of arcs Out-degree undirected network G(N,A) is a tree G(N,A) Cycle or circuit is a connected containing all n Incident arc Connected nodes subgraph having no nodes of N Connected Adjacent nodes undirected graph cycles Length of a path S Adjacent arcs Strongly A tree having t L ( S ) = l ( i , j ) nodes contains (t-1) ( i , j ) S Path connected Degree of a node directed graph edges d(x,y), d(i,j) Subgraph Shortest Path Problem Node Labeling Algorithm: Dijkstra Find the shortest path between two Shortest path from a node nodes, starting at Node O and ending k =1, start at origin node at Node D. At the end of iteration k , the set of k CLOSED NODES consists of the k closest _ O : O rigin node nodes to the origin. _ D : D estination node Each OPEN NODE adjacent to one or more closed nodes has our current 'best More generally: find least cost path guess' of the minimal distance to that node .
(MST) Problem Assume an undirected graph Problem: Find a shortest length contains (n-1) links.

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