1. Network Layer4-1 Spanning trees r Suppose you have a connected undirected graph m Connected: every node is reachable from every other node m Undirected: edges do not have an associated direction r...then a spanning tree of the graph is a connected subgraph in which there are no cycles A connected, undirected graph Four of the spanning trees of the graph

2. Network Layer4-2 Finding a spanning tree r To find a spanning tree of a graph, pick an initial node and call it part of the spanning tree do a search from the initial node: each time you find a node that is not in the spanning tree, add to the spanning tree both the new node and the edge you followed to get to it An undirected graphOne possible result of a BFS starting from top One possible result of a DFS starting from top

3. Network Layer4-3 Minimizing costs r Suppose you want to supply a set of houses (say, in a new subdivision) with: m electric power m water m sewage lines m telephone lines r To keep costs down, you could connect these houses with a spanning tree (of, for example, power lines) m However, the houses are not all equal distances apart r To reduce costs even further, you could connect the houses with a minimum-cost spanning tree

4. Network Layer4-4 Minimum-cost spanning trees r Suppose you have a connected undirected graph with a weight (or cost) associated with each edge r The cost of a spanning tree would be the sum of the costs of its edges r A minimum-cost spanning tree is a spanning tree that has the lowest cost AB ED FC 16 19 2111 33 14 18 10 6 5 A connected, undirected graph AB ED FC 16 11 18 6 5 A minimum-cost spanning tree

5. Network Layer4-5 Small Example

6. Network Layer4-6 Why Multicast r When sending same data to multiple receivers m better bandwidth utilization m less host/router processing m quicker participation r Application m Video/Audio broadcast (One sender) m Video conferencing (Many senders) m Real time news distribution m Interactive gaming

7. Network Layer4-7 Unicast/Multicast 128.146.222.0/24128.146.226.0/24 128.146.116.0/24128.146.199.0/24

8. Network Layer4-8 Unicast 128.146.222.0/24128.146.226.0/24 128.146.116.0/24 Receivers 128.146.199.0/24 Receiver Sender

9. Network Layer4-9 Multicast 128.146.222.0/24128.146.226.0/24 128.146.116.0/24 Receivers 128.146.199.0/24 Receiver Sender

10. Network Layer4-10 Two Major Issues r Who are the multicast members r How to send the packets to the members

11. Network Layer4-11 IGMP Host informs router with IGMP report 224.2.127.254 Designated router queries LAN for group membership 224.0.0.1

12. Network Layer4-12 IGMP – Joining a group Example : R joins to Group 224.2.0.1 R sends IGMP Membership-Report to 224.2.0.1 DR receives it. DR will start forwarding packets for 224.2.0.1 to Network A DR periodically sends IGMP Membership-Query to 224.0.0.1 (ALL-SYSTEMS.MCAST.NET) R answers IGMP Membership- Report to 224.2.0.1 R R: Receiver DR: Designated Router Data to 224.2.0.1 IGMP Membership-Report Network A Network B DR

13. Network Layer4-13 IGMP – Leaving a group Example : R leaves from a Group 224.2.0.1 R sends IGMP Leave-Group to 224.0.0.2 (ALL-ROUTERS.MCAST.NET) DR receives it. DR stops forwarding packets for 224.2.0.1 to Network A if no more 224.2.0.1 group members on Network A. Data to 224.2.0.1 R DR R: Receiver DR: Designated Router IGMP Leave-Group Network A Network B

14. Multicast Routing r Goal: find a tree (or trees) connecting routers having local mcast group members m tree: not all paths between routers used m source-based: different tree from each sender to rcvrs m shared-tree: same tree used by all group members Shared tree Source-based trees

15. Approaches for building mcast trees Approaches: r source-based tree: one tree per source m shortest path trees m reverse path forwarding r group-shared tree: group uses one tree m minimal spanning (Steiner) m center-based trees …we first look at basic approaches, then specific protocols adopting these approaches

16. Shortest Path Tree r mcast forwarding tree: tree of shortest path routes from source to all receivers m Dijkstra’s algorithm R1 R2 R3 R4 R5 R6 R7 2 1 6 3 4 5 i router with attached group member router with no attached group member link used for forwarding, i indicates order link added by algorithm LEGEND S: source

17. Reverse Path Forwarding if (mcast datagram received on incoming link on shortest path back to center) then flood datagram onto all outgoing links else ignore datagram  rely on router’s knowledge of unicast shortest path from it to sender  each router has simple forwarding behavior:

18. Reverse Path Forwarding: example result is a source-specific reverse SPT –may be a bad choice with asymmetric links R1 R2 R3 R4 R5 R6 R7 router with attached group member router with no attached group member datagram will be forwarded LEGEND S: source datagram will not be forwarded

19. Reverse Path Forwarding: pruning r forwarding tree contains subtrees with no mcast group members m no need to forward datagrams down subtree m “prune” msgs sent upstream by router with no downstream group members R1 R2 R3 R4 R5 R6 R7 router with attached group member router with no attached group member prune message LEGEND S: source links with multicast forwarding P P P

20. Shared-Tree: Steiner Tree r Steiner Tree: minimum cost tree connecting all routers with attached group members r problem is NP-complete r excellent heuristics exists r not used in practice: m computational complexity m information about entire network needed m monolithic: rerun whenever a router needs to join/leave

21. Center-based trees r single delivery tree shared by all r one router identified as “center” of tree r to join: m edge router sends unicast join-msg addressed to center router m join-msg “processed” by intermediate routers and forwarded towards center m join-msg either hits existing tree branch for this center, or arrives at center m path taken by join-msg becomes new branch of tree for this router

22. Center-based trees: an example Suppose R6 chosen as center: R1 R2 R3 R4 R5 R6 R7 router with attached group member router with no attached group member path order in which join messages generated LEGEND 2 1 3 1

23. Network Layer4-23 Overlay Multicast r Constructs Overlay Multicast Data Delivery Tree among Group Members r Intermediate Receiver can act as a Multicast Forwarder m Data is delivered by Unicast Tunneling Mechanisms, hop- by-hop basis