Slide Number 1AcknowledgementAdministrativeAdministrative Administrative Administrative Distributed Graph AlgorithmsRoutingPlan for TodaySlide Number 10Internet 5-Layer ModelInternet Routing Intra-AS Routing RevisitedInternet RoutingRouting: shortest path Shortest path Chandy&Misra’s Shortest Path (assumes static topology)Execution of Chandy-MisraShortest Path Internet Routing Algorithms Distance Vector RoutingExecution of DVRDistance Vector Routing ProtocolDistance Vector Routing DVRCounting to Infinity Link State Routing Link State ExecutionLink State Routing Link State Routing Protocol Link State Routing (Example)Link State Routing ProtocolSummaryLecture 16Distributed Graph (Routing) AlgorithmsSource: (1) Book “Distributed Systems: an Algorithmic Approach”, S. Gosh, Chapter 10.1-10.2.3 “Graph Algorithms” and (2) Chapter 3 in our textbookKlara NahrstedtCS 425/ECE 428/CSE 424Distributed Systems(Fall 2009)Acknowledgement• The slides during this semester are based on ideas and material from the following sources: – Slides prepared by Professors M. Harandi, J. Hou, I. Gupta, N. Vaidya, Y-Ch. Hu, S. Mitra. – Slides from Professor S. Gosh’s course at University o Iowa.Administrative• Homework 2 is graded and solutions are posted• Homework 3 is posted– Deadline: October 29, Thursday, 2 pm in class• Midterm is graded and solutions are posted• Midterm Re-grading Period by Instructor– October 27, 3:15-4pm – October 29, 3:15-4pm • No instructor office hours during the week of October 19-24 – (Instructor is at ACM International Conference on Multimedia 2009 in Beijing, China)Administrative • MP2 posted October 5, 2009, on the course website, – Deadline November 6 (Friday)– Demonstrations , 4-6pm, 11/6/2009 – You will need to lease one Android/Google Developers Phone per person from the CS department (see lease instructions)!!– Start early on this MP2 – Update groups as soon as possible and let TA know by email so that she can work with TSG to update group svn – Tutorial for MP2 planned for October 28 evening if students send questions to TA by October 25. Send requests what you would like to hear in the tutorial. – During October 15-25, Thadpong Pongthawornkamol ([email protected]) will held office hours and respond to MP2 questions for Ying Huang (Ying is going to the IEEE MASS 2009 conference in China)Administrative • MP3 proposal instructions – MP3 proposal is posted– You will need to submit a proposal for MP3 on top of your MP2 before you start MP3 on November 9, 2009– Deadline for Proposal: October 25, 2009, email proposal to TA– At least one representative of each group meets with instructor or TA during October 26-28 during their office hours ) watch for extended office hours during these days.• Instructor office hours: October 28 times 8:30-10amAdministrative • To get Google Developers Phone, you need a Lease Form – Fill out the lease form; bring the lease form to Rick van Hook/Paula Welch and pick up the phone from 1330 SC• Lease Phones: phones will be ready to pick up starting October 20, 9-4pm from room 1330 SC (purchasing , receiving and inventory control office)• Return Phones: phones need to be returned during December 14-18, 9-4pm in 1330 SCDistributed Graph Algorithms• why graph algorithms ? It is not a “graph theory” course!• many problems in networks can be modeled as graph problems– the topology of a distributed system is a graph– routing table computation uses the shortest path algorithm– efficient broadcasting uses a spanning tree– Max flow algorithm determines the maximum flow between a pair of nodes in a graph.Routing• Shortest path routing• Distance vector routing• Link state routing• Routing in sensor networks• Routing in peer-to-peer networks•Geographic routingPlan for Today• Routing algorithms – Chandy-Misra (distributed Bellman-Ford)– Distance vector– Link state– Interval routingThe Internet (Internet Mapping Project, color coded by ISPs)PCs,routers,switches…=nodeslinks=edgesInternet 5-Layer ModelInternet Routing AlgorithmsMessages (UDP) or Streams (TCP)ApplicationTransportInternetUDP or TCP packetsIP datagramsNetwork-specific framesMessageLayersUnderlying networkNetwork interfaceInternet RoutingIntra-AS Routing RevisitedSource: http://www.cisco.comInternet Routing• intra-AS routing– Open Shortest Path First(OSPF)– a link state protocol– (RFC 2328(1998) forIPv4, updated in RFC 5340(2008)• inter-AS routing– Border Gateway Protocol (BGP)– path vector protocol– makes routing decisions based on path, network policies and/or rule setsRouting: shortest path • most shortest path algorithms are adaptations of the classic Bellman- Ford algorithm. Computes shortest path if there are no cycle of negative weight • Let D(j) = shortest distance of j from initiator 0. Thus D(0) = 0 The edge weights w(j,k) can representlatency or distance or some other appropriate parameterShortest path revisiting Bellman Ford : basic idea Consider a static topology process 0 sends w(0,i), 0 to neighbor i {program for pi} upon receiving message (dist, k) if dist < Di then if parent ≠ k then parent := k fi; Di:= dist; send (Di+ w(i,j), i) to each neighbor j ≠ parent; if dist ≥ Dithen do nothingCurrent distanceCompute the shortestDistance to all nodesFrom an initiator nodeChandy&Misra’s Shortest Path (assumes static topology)/* D initialized to ∞, parent = i; deficit = 0, each message has format (distance, sender) */{for process 0}Process 0 sends w(0,i), 0 to neighbor i,deficit=|N(0)| ; /*N(0) set of successors of node 0; N(i) set of neighbors of node i */do deficit > 0 & ack, deficit:= deficit – 1 od;(deficit = 0 signals termination){for process i>0}do message(S,k) & S<D /* S value of distance received through message,D shortest distance between node 0 and i */ if parent ≠ k & deficit > 0 send ack to parent fi;parent:= k; D:=S;send(D + w(i,j),i) to each neighbor j ≠ parent;deficit:=deficit+|N(i)|;message(S,k) & S≥D send ack to sender; ack deficit:=deficit–1; deficit=0 & parent ≠ I send ack to parent; odExecution of Chandy-MisraShortest Path • an important issue is: how well do such algorithms perform when the topology changes? No real network is static! • let us examine distance vector routing and link state routing - adaptations of the shortest path algorithmInternet Routing Algorithms
View Full Document