1. Minimizing Broadcast Latency and Redundancy in Ad Hoc Networks
IEEE/ACM TRANSACTIONS ON NETWORKING
Volume 16, Issue 4, Aug. 2008
Rajiv Gandhi, Arunesh Mishra, and Srinivasan Parthasarathy
Presented by Pei-Wei Li

2. Outline Introduction Preliminaries Broadcast Algorithm
-Scheduling broadcasts for a single message
-Scheduling broadcasts for multiple massages
Distributed Implementation
Experimental evaluation

3. Introduction
Network wide broadcasting is a fundamental operation in ad hoc networks.
Redundant transmissions use up valuable resources in
the network such as power and bandwidth. Hence, it is
important to choose the intermediate nodes carefully
so as to avoid redundancy in transmissions.
Recently, real-time applications impose stringent end-
to-end latency requirements on the underlying
protocols.

4. Introduction In this paper, they present a simple distributed
collision-free broadcasting algorithm for
broadcasting a message.
Their algorithm extend to the case when multiple
messages are broadcast from multiple sources.
Their objective is to minimize the latency and the
number of transmissions in the broadcast.

5. Preliminaries 1.Network Model
They model an ad hoc network using a directed graph G=(V,E)
Each node u V has a transmission range range(u)
[rmin, rmax].
d( u, v) denote the Euclidean distance between u and v.
An arc (u,v) E iff v is in the transmission range of u, i.e., d(u,v) ≦ range(u).

6. Preliminaries 1.Network Model We assume that time is discrete.
Every message transmission occupies a unit time slot.
There is a collision at node w if w hears a message
from two transmitters at the same time.
A node w receives a message collision-free iff w hears the message without any collision.

7. Preliminaries 2.Problem Statement Given -a disk graph G=(V,E)
-a set of messages M={1,2,….,m}
-a set of sources for these messages:
sources={sj | sj is the source of message j }
A broadcast schedule specifies, for each message j
and each node i, the time at which node i receives
message j collision free and the time at which it
transmits message j .

8. Preliminaries 2.Problem Statement The goal is to compute a broadcast
schedule in which the latency and the
number of transmissions are minimized.
-The latency of the broadcast schedule is the first
time at which every node receives all messages.
-The number of transmissions is the total number
of times every node transmits any message.

9. Broadcast Algorithm 1.Scheduling broadcasts for a single message
The algorithm first constructs a broadcast tree Tb
rooted at source node s in which if a node u is a
parent of a node w, then u is responsible for
transmitting the message to w without any collision
at w.
It then schedules the transmissions so that every node receives the message collision free.
Let Ni(u) and No(u) denote the set of in-neighbors and out-neighbors of a node u V.

10. Broadcast Algorithm
The set of nodes is partitioned into primary nodes P and secondary nodes S. The nodes
in P form a dominating set in G.

11. Broadcast Algorithm P
BFS Tree P P
Broadcast Tree

12. Broadcast Algorithm
The transmissions are scheduled following a greedy strategy.
Any transmitting node u transmits at the
minimum time t that satisfies the following
three constraints:
1) u has received the message collision-free
before time t.
2) no node in C(u) is hearing any transmissions at
time t.
3) no node in No(u)\C(u) is receiving the message
collision free at time t.

13. Broadcast Algorithm

14. Broadcast Algorithm

15. Broadcast Algorithm 2.Scheduling broadcasts for multiple massages
Assume that the network has a uniform transmission range, i.e., rmin = rmax.
“One-to-all” broadcast algorithm schedules the
broadcast of multiple messages from a single source.
-Single Source Multiple Messages (SSMMs)
“All-to-all” broadcast algorithms schedule the
broadcast of multiple messages from many sources.
-intermediate source broadcast (ISB)
-multi-source broadcast (MSB)

16. Broadcast Algorithm Single Source Multiple Messages (SSMMs)
-The first stage computes the broadcast tree from s
using the algorithm BROADCASTTREE.
-The second stage computes a schedule for a
single message using a modified version of the
scheduling algorithm SCHEDULEBROADCASTS.
-The third stage efficiently computes a schedule for
every message in M ={1,2,….,m}.

17. Broadcast Algorithm

18. Broadcast Algorithm
Li is the set of nodes at level i in the BFS tree rooted at s. Let ti=ki, k is a constant. Any node in Li transmits the message between times ti+1and ti+1.

19. Broadcast Algorithm
j=1, t=1
j=2, t=3k+1

20. Broadcast Algorithm Why should s introduce a gap of 3k time
units between two successive message
transmissions?
-Any node in Li transmits the message
between times ti+1and ti+1.
-Transmissions from Li to Li+1
and transmissions from Li+3 to Li+4
can proceed simultaneously
without interfering with
each other. s k 1 2k 2 3k 3 4

21. Broadcast Algorithm Intermediate source broadcast (ISB)
-Stage1: Consider the shortest path pj from sj to an
arbitrarily chosen intermediate source s.
Every message j gets unicast along pj to s.
We ensure that these unicasts are collision free by a
greedy scheduling strategy that gives priority to
message j1 over j2 iff j1<j2 .
-Stage2: S uses SCHEDULEBROADCASTS_SSMM to broadcast all the messages.

22. Broadcast Algorithm Multi-source broadcast (MSB)
-Each source sj of the message computes a
broadcast tree Tj rooted at itself using the algorithm
BROADCASTTREE.
-Message j gets broadcast on tree Tj using the greedy
scheduling algorithm SCHEDULEBROADCASTS.
-Message j1 gets priority over j2 iff j1<j2.
This priority is enforced by scheduling j1 before j2.

23. Distributed Implementation
The single message broadcast algorithm can
be implemented using two DFS traversals.
(1)DFS traversal 1(to build the broadcast tree)
-The message source creates a token which visits
each node of the graph during its DFS traversal and
records the information about primary nodes and
their parents.
-When a node receives the token, it can compute its
parent and set of children.

24. Distributed Implementation
(1)DFS traversal 2 (to compute the schedule for a message)
-The source creates another token which does a
DFS traversal of the nonleaf nodes of the broadcast
tree and records the information about the receive
and transmit times of the nodes.
-The node computes its minimum possible collision-
free transmit time.

25. Distributed Implementation
The distributed implementations of our multiple message broadcast algorithms
(1)SSMM algorithm
-The first DFS computes the broadcast tree.
-In the second DFS, every transmitting node u computes
delay(u).
-S starts transmitting all the messages with a uniform
gap of 3k time units between two successive messages.

26. Distributed Implementation
(2)ISB
-Stage1:Computes the BFS tree rooted at s.
Every node knows its parent and its level and the maximum number of levels l in the BFS tree.
Let u Li be a node in the shortest path from sj to s.
u transmits the unicast message j at time
f( u, j)=3(j-1)+(l-i).
-Stage2 is the same as SSMM.

27. Distributed Implementation
Why should u Li transmits the unicast message j at time f( u, j)=3(j-1)+(l-i)?
l=5
level s 4 7 1 3 6 2 5 2 S4 3 1 4 S3 4 S1 S2

28. Distributed Implementation
(3)MSB
-It performs a DFS from each source sj to compute its broadcast tree and for each message j to compute its schedule.
ISB involves two DFS traversals and one BFS traversal, whereas MSB involves potentially 2M DFS traversals.
However, MSB has a much better broadcast latency compared to ISB

29. Experimental evaluation
The network nodes were placed uniformly at random within a square.
All the experiments were performed on strongly connected graphs.
All data points were averaged over 50 simulation runs.

30. Experimental evaluation
Performance metrics
-Broadcast latency is the maximum time taken by any node to receive the message.
-Approximation ratio is (latency/BFS depth).
-The number of transmissions is the total number of times every node transmits any message.

31. Experimental evaluation
1.Single Message Broadcast
Uniform Transmission Ranges

32. Experimental evaluation
1.Single Message Broadcast
Uniform Transmission Ranges

33. Experimental evaluation
1.Single Message Broadcast
Nonuniform Transmission Ranges

34. Experimental evaluation
1.Single Message Broadcast
Nonuniform Transmission Ranges

35. Related Work in our group
Energy-Efficient Multicast Routing in Mobile Ad Hoc Networks(92傅琳智學姊)
-Use Gauss-Markov mobility model to predict
positions and velocities of nodes.
-Design routing assignment of each destination.
-The goal is to minimize power consumption.
琳智學姊的work主要是energy efficient的Multicast routing。他利用Gauss-Markov mobility model 來預測Mobile ad hoc network中節點移動的pattern，就可以計算出結點在下個時間點的速率及可能的位置。有了節點的位置資訊，就可以算出從群撥來源端到各個群撥成員的routing path，而最後的目的是要將整個multicast過程中每個節點在傳輸data時所耗費的total power 最小化。

36. Related Work in our group
An Energy and Delay Efficient Scheduling
Algorithm for Data-Centric Wireless Sensor
Networks(93王弘翕學長)
-The node’s behavior is divided into receiving,
idling, sending, and sleeping.
-Construct a data aggregation tree and schedule
the activities of nodes on the tree.
-The goal is to minimize the total energy
consumption and a bounded end-to-end delay.
弘翕學長的work主要在wireless sensor network 中建立一個data aggregation tree，在tree上每個節點的activities可分為receiving, idling, sending, and sleeping. 時間可切割成依個個time slot，在data aggregation tree上的每個節點都會在某個time slot將data傳給neighbor。因為每個節點在進行不同activity時會有不同的power consumption，因此這個work的目標在於建立 data aggregation tree並且調整每個節點進行不同activity的時間以最小化整個sensor network的power consumption，同時也將data aggregation tree上所有data source將資料傳送到sink node的所耗費的時間限制再某個end-to-end delay requirement。

37. My Work
Construct a broadcast tree and schedule the transmission time of relay nodes to avoid collision and minimize the broadcast latency.
Every node’s mobility and power consumption will be considered.
我的work主要是在解決這篇paper所提出的問題也就是在wireless ad hoc network中建立broadcast tree並且schedule tree上每個relay node的transmission time，避免collision並將broadcast latency最小化，同時將琳智學姊有考慮到的node mobility因素加入，而且也考慮了學長和學姐的work裡energy efficient的議題，也就是限制每個節點在傳輸時所耗費的power。

38. Thanks for your listening!