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Efficient Broadcasting and Gathering in Wireless Ad-Hoc Networks
Melih Onus (ASU)Kishore Kothapalli (JHU)Andrea Richa (ASU)Christian Scheideler (JHU)
2005 International Symposium on Parallel Architectures, Algorithms and Networks, Las Vegas Nevada
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Ad-Hoc Networks
Mobile devices communicating via radio Network without centralized control Broadcasting: Sending a packet from a source
node to all nodes in the network Gathering: Sending one packet from a subset of
nodes to a single sink node in the network
3
Our Results
Near optimal algorithms for broadcasting and information gathering (time and work)
A realistic wireless communication model which takes into account– Different transmission & interference ranges– Non-uniformity of signal propagation of real antennas– Physical carrier sensing
4
Communication Models
Unit Disk Graph (UDG) Disk shaped transmission area
uR
vw
Packet Radio Network (PRN) Transmission Range = Interference Rangev
u
w
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Communication model
u
v
w
rt
ri
For a given transmission range rt, transmission area of v is
{ uV | c(v,u) rt }
Transmission range, interference area via cost function c
For given interference range ri, interference area of v is
{ uV | c(v,u) ri }
Cost Function:
c(u,v) [(1- )d(u,v), (1+ )d(u,v)]
d(u,v) is Euclidean distance [0,1), depends on the environment
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Communication model (cont.)
u
v
w
rt
ri
If c(v,u) ≤rt then v is guaranteed to receive the message from u provided no other node w with c(v, w) ≤ ri also transmits at the same time.
rt: Transmission rangeri: Interference range
If c(v,w) ≤ ri, node w can cause interference at node v.
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Physical Carrier Sensing
These ranges grow monotonically in both the sensing threshold T and the transmission power.
ursi(T)
v
w rst(T): Carrier sense transmission (CST) range
rst(T)
rsi(T): Carrier sense interference (CSI) range
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Constant density spanner
Constant density spanner: Given a graph G find a sparse subgraph G’ of G such that distance between any two nodes in G’ is less than a constant factor of original distance.
Active node
Inactive node
Gateway node
Gateway edge
Other edges
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Constant density spanner (cont.)
Active nodes form a maximal independent setGateway nodes connect active nodes which are within 2 or 3 hops from each other
Active node
Inactive node
Gateway node
Gateway edge
Other edges
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Motivation
Previously proposed broadcasting and gathering algorithms will not work for the communication model that we have considered.
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s( )(( ))
Isolated Broadcasting
Active node
Inactive node
Gateway node
Gateway edge
Other edges
Firstly, node s sends out the broadcast message.
((( ))) vu
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message
CTS
RTS
Isolated Broadcasting (cont.)
If u is a gateway node and has already received the message, it sends out an RTS signal with probability p.
If v is an active node or a gateway node and v has not received the broadcast message yet, then v checks if it correctly received an RTS signal. If so, v sends out a CTS signal.
If v is a gateway node and sent out a RTS signal, then v checks if it received a CTS signal. If so, v sends out the broadcast message.
svu
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Isolated Broadcasting (cont.)
Active node
Inactive node
Gateway node
Gateway edge
Other edges
sv
u
(( ))((( )))( )
If node v:– is an active node
– received the broadcast message in the previous round
– it is the first time it received the broadcast message Then, it sends out the broadcast message.
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Our Results
D(s): diameter with respect to s W(s): minimum work for broadcast
The broadcast algorithm needs O(D(s)+log n) rounds, with high probability, to deliver the broadcast messages to all nodes.
The broadcast algorithm needs O(W(s)) work Extendable to multiple broadcasts
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Building Gathering Tree T(s)
We select a shortest path tree rooted at s on the spanner graph by running a modified Bellman-Ford type algorithm that takes into account message interference.
In order to show that this RTS/CTS scheme works efficiently, it is crucial to note that the spanner is of constant density: Hence a constant number of RTS/CTS handshakes are enough to guarantee the successful delivery of a message w.h.p..
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RTSroute m.
Building Gathering Tree T(s) (cont.)
CTSs
vu
Firstly, node s sends out the route message.
<0> <1>(( ))((( )))( )
If the shortest path estimate d'(s,u) is not infinite and u needs to broadcast the latest update on d’(s,u), then u sends a RTS signal with probability p
If v received an RTS signal then v sends a CTS signal.
If u received a CTS signal, u sends out the route message.
<2>
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Building Gathering Tree T(s) (cont.)
svu
<0> <1>
Each node u has a label which is the shortest path distance to sink node.
<2>
<3>
<3><4>
<4>
<5>
<5>
<6>
<6> <7>
Each node u has a parent node which is the node that node u received the route message
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I-RTS
Gathering on Tree T(s) (Inactive Nodes)
Active node
Inactive node
Gateway node
Gateway edge
Other edges
If w is inactive and has a packet to send and w is awake then w sends a I-RTS signal to its parent with a probability 1/2.
s
w
Inactive nodes have a state {asleep, awake}
v
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Gathering on Tree T(s) (Inactive Nodes)
Active node
Inactive node
Gateway node
Gateway edge
Other edges
s
w
v
If v is active; v receives an I-RTS signal, send an I-CTS signal v senses a busy channel, send a collision message v senses a free channel, send a free message
I-RTS
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Gathering on Tree T(s) (Inactive Nodes)
Active node
Inactive node
Gateway node
Gateway edge
Other edges
s
w
v
If w is inactive; w receives an I-CTS signal, send the packet w receives a collision message, become asleep with p=1/2 w receives a free message, become awake
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Gathering on Tree T(s) (Active Nodes)
Active node
Inactive node
Gateway node
Gateway edge
Other edges
If v is active and has a message to send, then v sends the message to its parent.
sv
u
message
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RTS
Gathering on Tree T(s) (Gateway Nodes)
Active node
Inactive node
Gateway node
Gateway edge
Other edges
If u is a gateway node and has a non-empty queue then u sends an RTS message containing the id of its parent with probability p.
If u receives a CTS message from its parent, then u sends the message to its parent.
If an active node receives an RTS message containing its id, it sends a CTS message.
sv
u
CTS
message
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Our Results
: maximum density of inactive nodes m: number of messages W’(s): the optimal work
A gathering tree T(s) with sink node s, the information gathering algorithm presented above needs O(m+(logn)(log)+D(s)+logn) time steps w.h.p..
Once a stable gathering tree has been constructed, the gathering protocol described above needs O(W’(s)) work