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Spanning%20trees

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reverse path forwarding. group-shared tree: group uses one tree. minimal ... Reverse ... Reverse Path Forwarding: pruning. forwarding tree contains subtrees with no ... – PowerPoint PPT presentation

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Title: Spanning%20trees


1
Spanning trees
  • Suppose you have a connected undirected graph
  • Connected every node is reachable from every
    other node
  • Undirected edges do not have an associated
    direction
  • ...then a spanning tree of the graph is a
    connected subgraph in which there are no cycles

2
Finding a spanning tree
  • 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

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

4
Minimum-cost spanning trees
  • Suppose you have a connected undirected graph
    with a weight (or cost) associated with each edge
  • The cost of a spanning tree would be the sum of
    the costs of its edges
  • A minimum-cost spanning tree is a spanning tree
    that has the lowest cost

5
Small Example
6
Why Multicast
  • When sending same data to multiple receivers
  • better bandwidth utilization
  • less host/router processing
  • quicker participation
  • Application
  • Video/Audio broadcast (One sender)
  • Video conferencing (Many senders)
  • Real time news distribution
  • Interactive gaming

7
Unicast/Multicast
128.146.116.0/24
128.146.199.0/24
128.146.222.0/24
128.146.226.0/24
8
Unicast
128.146.116.0/24
128.146.199.0/24
Receiver
Sender
128.146.222.0/24
128.146.226.0/24
Receivers
Receiver
9
Multicast
128.146.116.0/24
128.146.199.0/24
Receiver
Sender
128.146.222.0/24
128.146.226.0/24
Receivers
Receiver
10
Two Major Issues
  • Who are the multicast members
  • How to send the packets to the members

11
IGMP
224.0.0.1
224.2.127.254
Designated router queries LAN for group membership
Host informs router with IGMP report
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

IGMP Membership-Report
R
Network A
DR
Data to 224.2.0.1
Network B
R Receiver DR Designated Router
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.

IGMP Leave-Group
R
Network A
DR
Data to 224.2.0.1
Network B
R Receiver DR Designated Router
14
Multicast Routing
  • Goal find a tree (or trees) connecting routers
    having local mcast group members
  • tree not all paths between routers used
  • source-based different tree from each sender to
    rcvrs
  • shared-tree same tree used by all group members

Shared tree
15
Approaches for building mcast trees
  • Approaches
  • source-based tree one tree per source
  • shortest path trees
  • reverse path forwarding
  • group-shared tree group uses one tree
  • minimal spanning (Steiner)
  • center-based trees

we first look at basic approaches, then specific
protocols adopting these approaches
16
Shortest Path Tree
  • mcast forwarding tree tree of shortest path
    routes from source to all receivers
  • Dijkstras algorithm

S source
LEGEND
R1
R4
router with attached group member
R2
router with no attached group member
R5
link used for forwarding, i indicates order
link added by algorithm
R3
R7
R6
17
Reverse Path Forwarding
  • rely on routers knowledge of unicast shortest
    path from it to sender
  • each router has simple forwarding behavior
  • if (mcast datagram received on incoming link on
    shortest path back to center)
  • then flood datagram onto all outgoing links
  • else ignore datagram

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

19
Reverse Path Forwarding pruning
  • forwarding tree contains subtrees with no mcast
    group members
  • no need to forward datagrams down subtree
  • prune msgs sent upstream by router with no
    downstream group members

LEGEND
S source
R1
router with attached group member
R4
router with no attached group member
R2
P
P
R5
prune message
links with multicast forwarding
P
R3
R7
R6
20
Shared-Tree Steiner Tree
  • Steiner Tree minimum cost tree connecting all
    routers with attached group members
  • problem is NP-complete
  • excellent heuristics exists
  • not used in practice
  • computational complexity
  • information about entire network needed
  • monolithic rerun whenever a router needs to
    join/leave

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

22
Center-based trees an example
Suppose R6 chosen as center
LEGEND
R1
router with attached group member
R4
3
router with no attached group member
R2
2
1
R5
path order in which join messages generated
R3
1
R7
R6
23
Overlay Multicast
  • Constructs Overlay Multicast Data Delivery Tree
    among Group Members
  • Intermediate Receiver can act as a Multicast
    Forwarder
  • Data is delivered by Unicast Tunneling
    Mechanisms, hop-by-hop basis
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