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Networks 1: Shortest path problem - MIT OpenCourseWare

1 April 11, 2013 Introduction to Networks 2 Quotes for today "A journey of a thousand miles begins with a single step." -- Confucius You cannot travel the path until you have become the path itself -- Buddha 3 Network Models Optimization models Can be solved much faster than other LPs Applications to industrial logistics, supply chain management, and a variety of systems Today s lecture: introductory material, Eulerian tours, the Shortest Path problem Application of Network Models: 4 Notation and Terminology Note: Network terminology is not (and never will be) standardized.

28 Eulerian cycle: a closed walk that passes through each arc exactly once Degree of a node = number of arcs incident to the node Necessary condition: each node has an even degree. Why necessary?The degree of a node j is twice the number of times j …

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