Regional Consecutive Leader Election
In Mobile Ad-Hoc Networks
Hyun Chul Chung*, Peter Robinson**, Jennifer L. Welch*
* Texas A&M University
** Vienna University of Technology
http://parasol.tamu.edu
Motivation (1)
• Recent oil spill in the Gulf of Mexico :
Source : www.free-download-blog.com
Seaswarm robot prototype
Source : www.computerworld.com
• Deploying seaswarm robots for clean up.
(Courtesy of MIT)
• By having a leader robot, non-conflicting decisions/instructions can be
made (guide robots to areas where oil spill is concentrated, etc).
• Since robots may become damaged, the process of electing a leader
should be consecutive.
2
Motivation (2)
• Leader election.
• Mobile ad-hoc networks.
• Region
(w/ bounded communication diameter)
leader
• “Regional Consecutive Leader Election” (RCLE) problem.
• Other applications : Deploying search and rescue robots at disaster sites.
3
System Model (1)
1
Out
2
3
In
7
8
4
5
6
• Mobile nodes communicating via wireless broadcast.
• Leader election in a single fixed geographical region.
• Exact time and location information (e.g. GPS).
4
System Model (2)
• Nodes execute in synchronous rounds of communication and computation.
• Such rounds can be guaranteed by having bounded 1-hop message
delay and exact time information which can be provided by, for instance,
the Abstract MAC Layer [Kuhn et al. 2009] and the GPS clock.
• Each round begins by broadcasts by nodes.
• Continues with nodes receiving certain broadcasts.
• At the end of each round, each node uses its current state and the set
of messages received during the round to change its state and decide
what to broadcast at the beginning of the next round.
r
r+1
r+2
5
System Model (3)
• Nodes have a (common) communication
radius.
• Just-In-Time (JIT) path starting at round r
from nodes v0 to vk of length k:
round
round
round
r+(k-1)
r+1
r
v0
vk
v2
v1
• A sequence of nodes v0, v1, ... , vk
such that for all i : 0 ≤ i ≤ k-1
• vi and vi+1 are live and within
communication radius of each other
throughout round r+i.
vk-1
v21k is in the region and within
comm. radius of v10k-1throughout
throughout
round r+1
rr+(k-1)
: : :
v21k receives v10k-1
’s’smessage
message
• vi is in the region at the beginning of r+i.
• vi+1 is in the region throughout round r+i.
6
System Model (4)
• We assume D-connectedness:
• For any pair of nodes p and q, and
every round r:
p
≤D
• If p is in the region at the beginning
of r and live throughout r, and
• If q is live and in the region
throughout [r, r+D-1], then
q
D rounds
• There exists a JIT path starting at r
from p to q of length at most D.
• We further assume that D is known to all
nodes in the system.
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The RCLE Problem (1)
3
1
7
2
8
4
5
6
• Goal : Electing a leader within a region.
• Mobility and failures require consecutive leader election:
• Leader could exit the region.
• Any node (including the leader) might crash.
8
The RCLE Problem (2)
• An algorithm solves the RCLE problem if...
• (Agreement) : All nodes in the region that elect a leader elect the
same leader.
• (Validity) : If some live node p in the region considers some node q as
a leader, then node q must have been in the region recently.
• (Termination) : If some live node remains in the region for a sufficiently
long period of time, then it must elect a leader.
• (Stability) : Decision is irrevocable unless leader crashes or leaves
the region.
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The RCLE Algorithm (1)
• Once a leader is elected...
r
q
LM
LM
LM
p
s
• The leader generates a “leader” message
every D rounds
• Message propagation is ensured by the
“relaying” message communication pattern
employed
• Every node sends the contents of its
message buffer at every round.
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The RCLE Algorithm (2)
• Two situations in which a node p should elect
(or re-elect) a leader:
q
LM
p
leader = r
s
r
• p has chosen a leader but fails to receive
a leader message in a timely fashion.
• leader must have left the region or
crashed.
• p enters the region.
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The RCLE Algorithm (3)
• In order to elect (or re-elect) a leader
• p generates an “instance” message.
r
q
IM
IM
IM
p
• If, during the next 2D rounds, p does not
receive a leader message or an instance
message from a node that entered the
region earlier than p did
s
• p elects itself as the leader.
wait 2D rounds
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The RCLE Algorithm (4)
• In order to elect (or re-elect) a leader (continued)
• If p receives a leader message before
2D rounds elapse
q
LM
p
r
• p adopts the generator of the leader
message as its leader
s
waiting
leader2D
= rrounds
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The RCLE Algorithm (5)
• In order to elect (or re-elect) a leader (continued)
LM
r:IM
q
p:IM
q:IM
p:IM
p:IM
p
leader
=2D
r
waiting
candidate
wait for
r’sleader
leader
rounds
=msg
r
r
entered region
the earliest
s
s:IM
• If, during those 2D rounds, p receives one
or more instance messages that were
generated by nodes that entered the region
earlier than p did
• p sets the generator that entered the
earliest as its “candidate leader”
• p then waits for a leader message from
the candidate leader
• If p receives the leader message from
the candidate leader in a timely fashion,
then p elects that node as its leader
• Otherwise, p initiates a new instance14
message
The RCLE Algorithm (6)
• The algorithm...
• Does not rely on...
• Knowledge of the number of nodes in the system.
• Common start up time.
• Relies on the knowledge of the bounded communication diameter of
the region.
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Bounds
• Each node has a leader variable (node p’s leader variable : leaderp).
• Nodes elect the leader by setting the leader variable.
• (Termination)
• If some node p stays in the region for (6D-2)Ne + D rounds it will elect
itself as the leader assuming that no other node elected itself as the
leader during this period (Ne : number of nodes in the region when p
entered the region)
• (Validity)
• If leaderp = q at round r, then there exists a round in [r-2D+1,r] where
node q is live and in the region.
• (Stability)
• If leaderp = q at round r1 and leaderp ≠ q at round r2 where r1 < r2,
then there exists a round in [r1-2D+1, r2] where node q has either
crashed or left the region.
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A Condition on Mobility
• We restrict the nodes to follow a condition on
mobility:
C
S (v0)
• Assume for any node (S) and
any position (F) in the region
• there exists a sequence of nodes
S = v0, v1, ... , vk
such that for all i : 0 ≤ i ≤ k-1
• vi broadcasts at round r+i,
• vi and vi+1 are within communication
radius of each other throughout r+i
and when vi+1 broadcasts it lies
within the shaded area of the figure,
• Position F is within the
communication radius of vk
δ
F
C
δ v1v1
δ
v2
region
δ : minimum progress
C : communication radius
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Calculation of D (1)
• Considering information propagation from
S to F
A
S (v0)
• the worst case position of v1 when it
broadcasts will be either point A or B
C
F
δ
B
• The distance between F and A (resp. B) is
• less than the distance between S and F.
• can be calculated with the distance
between S and F.
δ : minimum progress
C : communication radius
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Calculation of D (2)
• Recursive !
• Consider our single fixed region to be a
rectangle where the worst case distance
between any source and destination pair is L:
• We obtain D by recursively applying the
above method until the information gets
close enough (within communication
radius) to the destination.
• D : depth of recursion
G
region
S (v0)
C
F
C
δ
Bδ
P
H
C
δ : minimum progress
L radius
C :Gcommunication
H
C
δ
δ
δ : minimum progress
C : communication radius
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Related Work (1)
• Leader election in mobile ad-hoc environments
• Using geographical information
• [Kuhn et al. 2009] :
• Entire geographical space is divided into single-hop regions where
leader is elected for each region and these leaders form a leader
backbone.
• We consider a single fixed region with multi-hop communication.
• [Hatzis et al. 1999] :
• Elects leader by node encountering each other.
• Entire space is divided into subspaces where nodes encounter each
other by falling into the same subspace.
• Probabilistic analysis considering movement of nodes as random
walks.
• We provide a condition on mobility that gives a deterministic bound
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on message propagation.
Related Work (2)
• Not using geographical information
• [Boukerche & Abrougui 2006], [Malpani et al. 2000], [Ingram et al. 2009],
[Masum et al. 2006], [Parvathipuram et al. 2004], [Vasudevan et al. 2004] :
• All consider networks that can have an arbitrarily large communication
diameter.
• Our approach considers leader election in a region with bounded
communication diameter which is a better fit for situations when
leader election is needed only among nearby nodes.
• [Brunekreef et al. 1996] :
• Considers leader election in a 1-hop network in which messages are
received instantaneously.
• Our approach considers multi-hop networks.
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Summary and Future Work
• Introduced the Regional Consecutive Leader Election (RCLE) problem.
• Provided an algorithm that solves the RCLE problem when D-connectedness
holds.
• Gave a condition on mobility that ensures D-connectedness.
• Future Work
• Improved algorithm : better time and message complexity.
• better than O(nD) time (from initiating an instance message to electing
a leader) where n is the total number of nodes in the system.
• better than O(nD) messages per node per round.
• Weaker mobility conditions that guarantee D-connectedness.
• Lower bounds for the RCLE problem.
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Have a nice flight back home !
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