This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Introduction to Mathematical Programming IE406 Lecture 16 Dr. Ted Ralphs IE406 Lecture 16 1 Reading for This Lecture Bertsimas 7.17.3 IE406 Lecture 16 2 Network Flow Problems Networks are used to model systems in which a commodity or commodities must be transported from one or more supply points to one or more demand points along defined pathways. These models occur naturally in many contexts. Transportation Logistics Telecommunications Network flow problems are defined on graphs that define the structure of the pathways in the network. IE406 Lecture 16 3 Undirected Graphs An undirected graph G = ( N, E ) consists of A finite set of nodes N representing the supply and demand points. A set E of unordered pairs of nodes called edges representing the pathways joining pairs of nodes. We say that the edge { i, j } is incident to nodes i and j and i and j are its endpoints . The degree of a node is the number of edges incident to it. The degree of a graph is the maximum of the degrees of its nodes. IE406 Lecture 16 4 Basic Definitions (Undirected) A walk is a finite sequence of nodes i 1 , . . . , i t such that { i k , i k +1 } E k = 1 , 2 , . . . , t 1 . A walk is called a path if it has no repeated nodes. A cycle is a path with i 1 = i t , t > 2 . An undirected graph is said to be connected if for every pair of nodes i and j , there is a path from i to j ....
View
Full
Document
This note was uploaded on 08/06/2008 for the course IE 406 taught by Professor Ralphs during the Fall '08 term at Lehigh University .
 Fall '08
 Ralphs

Click to edit the document details