Outline Introduction Six Degrees of Separation P2P Networks OSI Model References. Graphs and Networks. Aravind Ranganathan

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1 Graphs and Networks Aravind Ranganathan PhD Candidate, University of Cincinnati Alumni, SSNCE August 27, 2007

2 Outline Modeling Networks as Graphs Six degrees of separation P2P Networks OSI Layers Wireless Networks

3 Outline Modeling Networks as Graphs Six degrees of separation P2P Networks OSI Layers Wireless Networks

4 Definitions Network: Any interconnected group or system Examples: Human Networks Computer Networks Biological Networks Graph: Collection of Nodes and Edges

5 Definitions Network: Any interconnected group or system Examples: Human Networks Computer Networks Biological Networks Graph: Collection of Nodes and Edges Why model networks as graphs?

6 Why Model Networks as Graphs? To solve the problems theoretically!!

7 Why Model Networks as Graphs? Facility Location Problem: Where to place 10 new Fresh shops around the city?

8 Why Model Networks as Graphs? Some Well Known Problems (and Algorithms): Traveling Salesman Problem Minimum Spanning Trees: Kruskal / Prim s Algorithm Shortest Path: Bellman-Ford / Dijkstra / Floyd s Algorithm Perfect Matching: Hungarian Algorithm Max-Flow/Min-Cut: Ford-Fulkerson s Algorithm

9 Why Model Networks as Graphs? Some Well Known Problems (and Algorithms): Traveling Salesman Problem Minimum Spanning Trees: Kruskal / Prim s Algorithm Shortest Path: Bellman-Ford / Dijkstra / Floyd s Algorithm Perfect Matching: Hungarian Algorithm Max-Flow/Min-Cut: Ford-Fulkerson s Algorithm Not all problems have polynomial time complexity :(

10 6 Degrees of Separation Idea that everyone is no more than 6 steps away from any person on Earth Small world phenomenon

11 Small World Experiments Stanley Milgram s Experiments ( 67) To determine the probability that two randomly selected people would know each other Selected several pairs of random individuals (start and end) Each person to forward the letter only to a friend Human Society is a small world type network!! Duncan Watts recreating Milgram s Experiment ( 01) Milgram s experiment on the internet using Degree of separation was still 6!!

12 Small World Experiments Stanley Milgram s Experiments ( 67) To determine the probability that two randomly selected people would know each other Selected several pairs of random individuals (start and end) Each person to forward the letter only to a friend Human Society is a small world type network!! Duncan Watts recreating Milgram s Experiment ( 01) Milgram s experiment on the internet using Degree of separation was still 6!!

13 Theoretical basis Let: Then, Total Population = P, Avg. No. of friends per person = f, Degrees of separation = d. P = f d implies, d = ln P ln f If P=6 billion, for d=6, each person must know 42 people (approx) Note: 6 degree of separation is only in the average sense

14 Theoretical basis Let: Then, Total Population = P, Avg. No. of friends per person = f, Degrees of separation = d. P = f d implies, d = ln P ln f If P=6 billion, for d=6, each person must know 42 people (approx) Note: 6 degree of separation is only in the average sense

15 Six Degrees of Kevin Bacon Trivia game based on the small world phenomenon Any actor can be linked, through their film roles, to actor Kevin Bacon Figure: Kevin Bacon

16 6 Degrees - Examples - Kevin Bacon and Amitabh Bachchan Kevin Bacon has an Amitabh Bachchan number of 3. Kevin Bacon was in Sleepers ( 96) with Michael J. Burg Burg was in One-Third ( 06) with Greg D Agostino D Agostino was in Kabhi Alvida Naa Kehna ( 06) with Amitabh Bachchan

17 6 Degrees - Examples - Al Pacino and RajniKanth Al Pacino has a RajniKanth number of 3. Al Pacino was in Revolution ( 85) with Steven Berkoff Berkoff was in Bokshu the Myth ( 02) with Vineeth Vineeth was in Chandramukhi ( 05) with Rajnikanth

18 Peer-to-Peer Network Client-Client Architecture vs. Client-Server Architecture Distributed computer network Utilizes cumulative resources of nodes Popular uses: Digital content sharing Streaming audio, video, and realtime data

19 Napster By Shawn Fanning (and Sean Parker) on June 1, 1999 Sharing music (as.mp3) Central servers to maintain lists of connected systems and files they provided Eventually shutdown

20 BitTorrent P2P communications protocol by Bram Cohen ( 01) Each file is split into several chunks A Tracker maintains lists of the clients currently participating in the torrent Information stored in.torrent file To download the file Peer downloads the.torrent file Gets list of other peers sharing the file from Tracker Downloads new chunks from available peers Uploads downloaded chunks to other peers Reduces cost, More redundancy

21 BitTorrent Animation Coloured bars - Individual chunks of the file Chunks individually transferred from client to client Original seeder only sends out 1 copy of the file for all the clients to receive a copy

22 BitTorrent Animation Coloured bars - Individual chunks of the file Chunks individually transferred from client to client Original seeder only sends out 1 copy of the file for all the clients to receive a copy

23 BitTorrent Animation Coloured bars - Individual chunks of the file Chunks individually transferred from client to client Original seeder only sends out 1 copy of the file for all the clients to receive a copy

24 BitTorrent Animation Coloured bars - Individual chunks of the file Chunks individually transferred from client to client Original seeder only sends out 1 copy of the file for all the clients to receive a copy

25 BitTorrent Animation Coloured bars - Individual chunks of the file Chunks individually transferred from client to client Original seeder only sends out 1 copy of the file for all the clients to receive a copy

26 BitTorrent Animation Coloured bars - Individual chunks of the file Chunks individually transferred from client to client Original seeder only sends out 1 copy of the file for all the clients to receive a copy

27 Classification of Networks Computer Networks: LANs, MANs and WANs Wired vs. Wireless Examples: Internet IEEE Networks Ad-hoc Networks Sensor Networks Mesh Networks Cellular Networks

28 Classification of Networks Computer Networks: LANs, MANs and WANs Wired vs. Wireless Examples: Internet IEEE Networks Ad-hoc Networks Sensor Networks Mesh Networks Cellular Networks

29 OSI Model Open Systems Interconnection Basic Reference Model Abstract model of networking and set of concrete protocols Networking system is divided into layers Within each layer, one or more entities implement its functionality Each entity interacts only with layer immediately beneath it, provides facilities for the layer above it

30 Snail Mail Scenario Karthik from Chennai and Amit from Delhi are Pen pals. Letter from Karthik to Amit 1 Karthik writes a letter and addresses it to Amit 2 Karthik posts the letter in the postbox 3 Letter collected from postbox, reaches local Post Office (PO) 4 PO sorts the letter and places it with other letters to Delhi 5 Letters to Delhi are physically transported to Delhi PO 6 PO postman delivers Karthik s letter to Amit s house 7 Amit reads the letter from Karthik

31 Advantages of the Layered Approach Data Abstraction Easy to add / modify functionality Interoperability among vendors

32 OSI Layers Appln, Presentation, Session Layers: Provides network services to user applns Transport Layer Responsible for end-to-end data txn Network Layer Routing data from one node to another Data Link Layer Physical txn of data in a link Physical Layer Sends & receives in bits

33 References Wikipedia Six degrees of separation P2P Networks OSI Model Kevin Bacon Oracle: links.html

34 Contact www: rangana