Slides4 - Graph Theory and Topology Design Graduate...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Graph Theory and Topology Design David Tipper Associate Professor Graduate Telecommunications and Networking Program University of Pittsburgh tipper@tele.pitt.edu Slides 4 http://www.sis.pitt.edu/~dtipper/2110.html • Top down network design project approach should follow three phases: – Conceptual Model Top Down Network Design Approach • Objectives, Requirements, Constraints – Logical Model • Technology, network graph, node location, link size, etc. (where algorithms are used to minimize cost) – Physical Model • Specific hardware/software implementations Telcom 2110 2 • (e.g., wiring diagram, repeater locations, etc.) • Focus on Algorithms for Logical Model Design – Graph Theory – Optimization
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Graphs • Telecommunication and computer networks are naturally represented by graphs • A graph G = (V, E) is a mathematical structure consisting of two sets V and E two sets and • Elements of V are called vertices (or nodes) –For example, switches, routers, crossconnects • Elements of E are called edges –Communication links are edges (wired or wireless) –Each edge has two endpoints Vertex V v v ) , ( 2 1 Telcom 2110 3 A B C D E F G V ={A,B,C,D,E,F,G} E = {(A,B),(A,C), (A,D), (B,C), …. , (F,G)} Edge Terminology • Networking tends to use notation G(N,L) instead of G(V, E) for a graph where N is set of nodes and L is set of links • A graph is simple if it has no loops or parallel edges. Loop • Link where both endpoints are the same node. Also called a self-loop. Parallel edges A collection of two or more links having identical ends. Also called a multi-edge. – Focus on simple graphs Degree of a node (vertex): d i – Number of links/edges out of a node (assuming same number of in and out links Telcom 2110 4 and out links) • Adjacent nodes/vertices: – Two nodes are adjacent if there is a link that has them as endpoints node degree d i = number of neighbor nodes of node i
Background image of page 2
3 A D F Terminology Cont. Example network: simple graph Degree of Node A d A = 3, Degree of Node E d E = 2 A and B are adjacent, A and E not B C E G • Can represent graph by Adjacency matrix A which is |N| x |N| matrix where Size of graph characterized by number of nodes |N| and number of links |L| Example network: |N| = 7, |L| = 10 ABCDEFG A- 111000 Telcom 2110 5 a ij = 1 if link exist between nodes i and j a ij = 0 otherwise B0 -10000 C1 1- 1001 D1 01 - 1 1 0 E0 001- 01 F0 0010- 1 G0 01011- A = Paths and Cycles • Path from node A to node Z : An alternating sequence of nodes and links, representing a continuous traversal from vertex A to vertex Z. • Trail: a path with no repeated edges. • Cycle: a path starting and ending on the same node • Connected graph: A graph in which every pair of distinct nodes has a path between them. • Weighted Graph: Telcom 2110 6 – A graph G(N,L) is weighted if there is a value w ij associated with each link l ij ɛ L • For example, link speed, cost, etc.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/26/2010 for the course SIS TElcom 211 taught by Professor Tipper during the Spring '10 term at Philadelphia.

Page1 / 36

Slides4 - Graph Theory and Topology Design Graduate...

This preview shows document pages 1 - 4. Sign up to view the full document.

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