lec14 - Networks Lecture 1 Amedeo R Odoni Thanks to Prof R...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Networks: Lecture 1 Amedeo R. Odoni November 15, 2006 * Thanks to Prof. R. C. Larson for some of the slides General Comments From continuous to a more “discretized” travel environment Enormous literature and variety of problems Transportation and logistics, urban services just two of the major areas of applications Level of detail of model depends on problem Numerous interpretations of “nodes” (“points”, “vertices”) and “arcs” (“links”, “edges”) Will concentrate on routing and location problems Will assume that efficient shortest path algorithms are available
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Outline and References Introduction Minimum Spanning Tree (MST) Chinese Postman Problem (CPP) Skim Sections 6.1 and 6.2, read Sections 6.3- 6.4.4 in Larson and Odoni Far more detailed coverage in (among others) Ahuja, R., T. L. Magnanti and J. B. Orlin, Network Flows, Prentice-Hall, 1993. Network with Terminology A B C D E Nodes B and D Directed Arc Undirected Arc
Background image of page 2
Examples of Nodes & Arcs Nodes/ Vertices/ Points Street intersections Towns Cities Electrical junctions Project milestones Arcs/ Edges/ Links Street segments Country roads Airplane travel time Circuit components Project tasks Network Terminology N = sets of nodes A = set of arcs G(N,A) Incident arc Adjacent nodes Adjacent arcs Path Degree of a node In-degree Out-degree Cycle or circuit Connected nodes Connected undirected graph Strongly connected directed graph Subgraph
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Network Terminology - con't. Tree of an Spanning tree of undirected network G(N,A) is a tree is a connected containing all n subgraph having no nodes of N cycles Length of a path S A tree having t L ( S ) = l ( i , j ) nodes contains (t-1) ( i , j ) S edges d(x,y), d(i,j) Shortest Path Problem Find the shortest path (more generally, least cost path) between two nodes, starting at Node O and ending at Node D. Dijkstra’s node labeling algorithm (essentially dynamic programming); one-to-all paths; all edge lengths are non-negative; O(n 2 ). Floyd’s algorithm; negative edge lengths OK (discovers negative cycles); all-to-all paths; non-obvious; O(n 3 ). Numerous variations and extensions: all-to-one; critical
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 25

lec14 - Networks Lecture 1 Amedeo R Odoni Thanks to Prof R...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online