# Spanning%20trees - PowerPoint PPT Presentation

View by Category
Title:

## Spanning%20trees

Description:

### 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

Number of Views:74
Avg rating:3.0/5.0
Slides: 24
Provided by: JimKurosea352
Category:
Tags:
Transcript and Presenter's Notes

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 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
Sender
128.146.222.0/24
128.146.226.0/24
9
Multicast
128.146.116.0/24
128.146.199.0/24
Sender
128.146.222.0/24
128.146.226.0/24
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
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 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
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
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
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
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

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
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