Regional Consecutive Leader Election In Mobile Ad-Hoc Networks

1. 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

2. Motivation (1) • Recent oil spill in the Gulf of Mexico : • Deploying seaswarm robots for clean up. • 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. Source : www.free-download-blog.com Seaswarm robot prototype Source : www.computerworld.com (Courtesy of MIT)

3. Motivation (2) • Leader election. • Mobile ad-hoc networks. • Region • (w/ bounded communication diameter) • “Regional Consecutive Leader Election” (RCLE) problem. • Other applications : Deploying search and rescue robots at disaster sites. leader

4. System Model (1) 3 7 Out In 8 2 1 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).

5. 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

6. 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: • 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. • vi is in the region at the beginning of r+i. • vi+1 is in the region throughout round r+i. round r+(k-1) round r+1 round r v0 v1 v2 vk-1 vk … v2 is in the region and within comm. radius of v1 throughout round r+1 : v2 receives v1’s message vk is in the region and within comm. radius of vk-1 throughout round r+(k-1) : vk receives vk-1’s message v1 is in the region and within comm. radius of v0 throughout round r : v1 receives v0’s message

7. System Model (4) • We assume D-connectedness: • For any pair of nodes p and q, and • every round r: • 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 • 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. p ≤ D q D rounds

8. The RCLE Problem (1) 3 7 8 2 1 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.

9. 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.

10. The RCLE Algorithm (1) • Once a leader is elected... • 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. r q LM LM LM s p

11. The RCLE Algorithm (2) • Two situations in which a node p should elect • (or re-elect) a leader: • 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. r q LM s p leader = r

12. The RCLE Algorithm (3) • In order to elect (or re-elect) a leader • p generates an “instance” message. • 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 • p elects itself as the leader. r q IM IM IM s p wait 2D rounds

13. The RCLE Algorithm (4) • In order to elect (or re-elect) a leader (continued) • If p receives a leader message before • 2D rounds elapse • p adopts the generator of the leader • message as its leader r q LM s p waiting 2D rounds leader = r

14. The RCLE Algorithm (5) • In order to elect (or re-elect) a leader (continued) • 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 instance • message LM r q r:IM entered region the earliest q:IM s p s:IM leader = r wait for r’s leader msg waiting 2D rounds candidate leader = r p:IM p:IM p:IM

15. 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.

16. 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.

17. A Condition on Mobility • We restrict the nodes to follow a condition on • mobility: • 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 C S (v0) F v1 δ C S (v0) S (v0) F F δ: minimum progress C : communication radius C v1 δ v1 v2 δ region region

18. Calculation of D (1) • Considering information propagation from • S to F • the worst case position of v1 when it • broadcasts will be either point A or 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. A S (v0) F C δ B δ: minimum progress C : communication radius

19. 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 S (v0) F C δ B δ: minimum progress C : communication radius G region C L S (v0) F H G H G L C C H δ B δ δ δ: minimum progress C : communication radius P

20. 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 providea condition on mobility that gives a deterministic bound • on message propagation.

21. 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.

22. 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.

23. Have a nice flight back home !