Efficient Broadcasting and Gathering in Wireless AdHoc Networks

1
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
2
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
v
w
u
R
Packet Radio Network (PRN) Transmission Range
Interference Range
5
Communication model

• Transmission range, interference area via cost
  function c

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

• For a given transmission range rt, transmission
  area of v is
• u?V c(v,u) ? rt

• For given interference range ri, interference
  area of v is
• u?V c(v,u) ? ri

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Communication model (cont.)
rt Transmission range ri Interference range

• If c(v,w) ri, node w can cause interference
  at node v.

• 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.

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Physical Carrier Sensing
rst(T) Carrier sense transmission (CST) range
rst(T)
rsi(T) Carrier sense interference (CSI) range

• These ranges grow monotonically in both the
  sensing threshold T and the transmission power.

14
8
Constant density spanner
Active node
Inactive node
Gateway node
Gateway edge
Other edges

• 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.

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Constant density spanner (cont.)
Active node
Inactive node
Gateway node
Gateway edge
Other edges

• Active nodes form a maximal independent set
• Gateway nodes connect active nodes which are
  within 2 or 3 hops from each other

10
Motivation

• Previously proposed broadcasting and gathering
  algorithms will not work for the communication
  model that we have considered.

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Isolated Broadcasting
Active node
Inactive node
s
u
Gateway node
v
( )
(( ))
((( )))
Gateway edge
Other edges

• Firstly, node s sends out the broadcast message.

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Isolated Broadcasting (cont.)

• If u is a gateway node and has already received
  the message, it sends out an RTS signal with
  probability p.

s
u
v
CTS
message
RTS

• 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.

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Isolated Broadcasting (cont.)
Active node
Inactive node
s
u
Gateway node
v
(( ))
((( )))
( )
Gateway edge
Other edges

• 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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Information Gathering

• Stage I Building Gathering Tree T(s)
• Stage II Gathering on Tree T(s)

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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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Building Gathering Tree T(s) (cont.)
Firstly, node s sends out the route message.
s
u
v
CTS
(( ))
((( )))
( )
lt1gt
lt0gt
RTS
route m.
lt2gt

• 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.

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Building Gathering Tree T(s) (cont.)
lt6gt
lt7gt
lt4gt
lt5gt
s
u
lt3gt
v
lt1gt
lt6gt
lt0gt
lt5gt
lt2gt
lt4gt
lt3gt

• Each node u has a label which is the shortest
  path distance to sink node.

• Each node u has a parent node which is the node
  that node u received the route message

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Gathering on Tree T(s) (Inactive Nodes)
Active node
Inactive node
s
Gateway node
v
Gateway edge
Other edges
I-RTS
w
Inactive nodes have a state asleep, awake
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.
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Gathering on Tree T(s) (Inactive Nodes)
Active node
Inactive node
s
Gateway node
v
Gateway edge
Other edges
I-RTS
w

• 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

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Gathering on Tree T(s) (Inactive Nodes)
Active node
Inactive node
s
Gateway node
v
Gateway edge
Other edges
w

• If w is inactive
• w receives an I-CTS signal, send the packet
• w receives a collision message, become asleep
  with p1/2
• w receives a free message, become awake

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Gathering on Tree T(s) (Active Nodes)
Active node
Inactive node
s
u
Gateway node
v
Gateway edge
message
Other edges
If v is active and has a message to send, then v
sends the message to its parent.
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Gathering on Tree T(s) (Gateway Nodes)
Active node
Inactive node
s
u
RTS
Gateway node
message
v
Gateway edge
CTS
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 an active node receives an RTS message
  containing its id, it sends a CTS message.

• If u receives a CTS message from its parent, then
  u sends the message to its parent.

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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

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Conclusions and Future work

• Algorithms for broadcasting and information
  gathering on a realistic model for wireless
  communication
• Node mobility and node faults
• Anycasting and multicasting