Multipoint Relaying for Flooding Broadcast Messages in Mobile Wireless Networks

1
Multipoint Relaying for Flooding Broadcast
Messages inMobile Wireless Networks
Authors Amir Qayyum, Laurent Viennot, Anis
Laouiti Publisher Proceedings of the 35th
Annual Hawaii International
Conference on System Sciences Present Min-Yuan
Tsai (???) Date September, 18, 2006
Department of Computer Science and Information
Engineering National Cheng Kung University,
Taiwan R.O.C.
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Outline

• 1. Introduction
• 2. Multipoint relaying
• 3. Complexity analysis on the
• computation of multipoint relays
• 4. Simulations
• 5. Conclusion

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Introduction

• Ad-hoc networks have an inherent capacity for
  broadcasting.
• A compromise for optimizing broadcast messages
  has to be made between a small number emissions
  and the reliability.
• Multipoint relaying is a technique to reduce the
  number of redundant re-transmissions while
  diffusing a broadcast message in the network.

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Requirements of a mobile wireless environment

• In mobile wireless networks, each of these
  two words put before us a list of requirements.
• The mobility implies the limited lifetime of
  neighborhood or topology information received at
  any time because of the movement of nodes.
• The wireless nature of the medium implies the
  limited bandwidth capacity available in a
  frequency band.
• Therefore, the requirements of these two
  environments are completely opposite to each
  other.

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Outline

• 1. Introduction
• 2. Multipoint relaying
• 3. Complexity analysis on the compution of
  multipoint relays
• 4. Simulations
• 5. Conclusion

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Flooding of broadcast messages in the network
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Flooding of broadcast messages in the network
(cont.)

• Pure flooding
• Advantage simple, easy to implement, a high
  probability
• Disadvantage broadcasting storm

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Heuristic for the selection of multipoint relays

• 1. Start with an empty multipoint relay set
  MPR(x)
• 2. First select those one-hop neighbor nodes in
  N(x) as
• multipoint relays which are the only
  neighbor of some
• node in N2 (x), and add these one-hop
  neighbor nodes
• to the multipoint relay set MPR(x)
• 3. While there still exist some node in N2 (x)
  which is not
• covered by the multipoint relay set
  MPR(x)
• (a) For each node in N(x) which is not in MPR(x),
  compute
• the number of nodes that it covers
  among the uncovered
• nodes in the set N2 (x)
• (b) Add that node of N(x) in MPR(x) for which
  this number is
• maximum.

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NP-completeness

• Multipoint Relay Given a network (i.e. the set
  of one-hop neighbors for each node), a node x of
  the network and an integer k, is there a
  multipoint relay set for x of size less than k ?
• Dominating Set Problem Given a graph (i.e. a set
  of nodes and a set of neighbors for each node)
  and a number k, is there a dominating set of
  cardinality less than k ? Where a dominating set
  is a set S of nodes such that any node of the
  graph is either in S or in the neighborhood of
  some node in S.

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NP-completeness (cont.)

• Let us make a copy of V and denote with a prime
  the copies x denotes the copy of x for any x ? V
  and S denotes the set of copies of the elements
  of any set S ? V (V denotes the set of all the
  copies). Let s be an element neither in V nor in
  V . Consider a network where the nodes are s ?
  V ? V and where the neighborhoods are the
  following
• N(s) V,
• N(x) x ?M(x) for x ? V ,
• N(x) x ?M(x) for x ? V

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Outline

• 1. Introduction
• 2. Multipoint relaying
• 3. Complexity analysis on the
• computation of multipoint relays
• 4. Simulations
• 5. Conclusion

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Formal definition

• If x is a node of the network, we denote
• 1) N(x) be the set of one-hop neighbors of x.
  (Here we consider
• that x N(x).)
• 2) (x) be the set of two-hop neighbors of x.
• A set S ? N(x) is a multipoint relay set for x if
  S covers N2(x).
• A multipoint relay set for a node x is optimal if
  its number of elements is minimal among all the
  multipoint relay set for x. We call this number
  the optimal multipoint relay number for x.

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Analysis of the Proposed Heuristic

• We prove that the heuristic computes a multipoint
  relay set of cardinality at most log n times the
  optimal multipoint relay number where n is the
  number of nodes in the network.
• Definition
• 1) S1 be the nodes selected in stage 2 of the
  above
• algorithm.
• 2) x1, . . . , xk be the nodes selected in stage
  3 (xi is the i-th
• added node).
• 3) S be a solution with minimal cardinality. (S1
  ? S, since any
• node in S1 is the only neighbor of some
  node in N2(s))
• 4) N12 be the set of nodes in N2(s) that are
  neighbors of some node in S1
• We will show that S-S1 log n S-S1 which
  implies that the computed solution is within a
  factor log n from the optimal.

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Analysis of the Proposed Heuristic

• We set N2 N2 - N12 , S S - S1, S S - S1
  and
• N(x) N(x) n N2 for each node x ? N. We
  associate a cost cy with each node y ? N2.
• We are going to show that for any node z in S,
  we have

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Analysis of the Proposed Heuristic

• Any node y ?N2 is the neighbor of some x ? S
  (remember that no node in S1 is a neighbor of y
  by definition). We can thus deduce

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Outline

• 1. Introduction
• 2. Multipoint relaying
• 3. Complexity analysis on the
• computation of multipoint relays
• 4. Simulations
• 5. Conclusion

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Simulations

• The objective of the simulations was to compare
  two types of algorithms for the diffusion of
  packets in the radio networks one is pure
  flooding technique, and the second is diffusion
  of packets using multipoint relays.
• For all the simulations, we considered a graph of
  1024 nodes placed on a 32x32 grid.
• Some assumptions that is the impact of error of
  reception on the diffusion of packets.
• The messages are broadcast messages which do not
  require an explicit acknowledgement to confirm
  the reception. Hence there was no retransmission
  when error of reception occurred
• There are no uni-directional links. Each link
  between a pair of nodes is a perfect
  bidirectional link

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Simulations (cont.)

• The only traffic exists in the network is that of
  the diffusion of broadcast packet
• Each node retransmits a packet (if it has to
  retransmit according to the protocol) only once
• There is a synchronization among the
  transmissions. Channel is time-slotted and each
  transmission takes one slot
• Each time a node transmits a packet, its one-hop
  neighbors receive this packet with probability P,
  where P is a percentage which lies between 0 and
  100.

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Simulations (cont.)
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Simulations (cont.)
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Simulations (cont.)
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Simulations (cont.)
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Simulations (cont.)
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Outline

• 1. Introduction
• 2. Multipoint relaying
• 3. Complexity analysis on the
• computation of multipoint relays
• 4. Simulations
• 5. Conclusion

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Conclusion

• Although the classic technique of pure flooding
  to diffuse a message in the network is more
  reliable and robust, it consumes a large amount
  of bandwidth as its cost.
• Multipoint relaying gives equally good results,
  with much less control traffic, when the errors
  of reception remains less than 20.
• In general, its a quite realistic assumption to
  consider these errors as less than 10 in a
  network.
• We can conclude that in the range of error rate
  which is most common, the multipoint relaying
  gives us quite satisfactory results .