1. http://parasol.tamu.edu 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. 2 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. 3 leader

4. System Model (1) Mobile nodes communicating via wireless broadcast. Leader election in a single fixed geographical region. Exact time and location information (e.g. GPS). InOut 4 8732 1 5 4 6

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 5

6. System Model (3) Nodes have a (common) communication radius. Just-In-Time (JIT) path starting at round r from nodes v 0 to v k of length k: A sequence of nodes v 0, v 1,..., v k such that for all i : 0 ≤ i ≤ k-1 v i and v i+1 are live and within communication radius of each other throughout round r+i. v i is in the region at the beginning of r+i. v i+1 is in the region throughout round r+i. round r 6 v 1 is in the region and within comm. radius of v 0 throughout round r : v 1 receives v 0 ’s message v 2 is in the region and within comm. radius of v 1 throughout round r+1 : v 2 receives v 1 ’s message v k is in the region and within comm. radius of v k-1 throughout round r+(k-1) : v k receives v k-1 ’s message v0v0 v1v1 v2v2 v k-1 round r+1round r+(k-1) vkvk …

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 q ≤ D 7 D rounds

8. The RCLE Problem (1) 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. 1 7 4 5 2 6 3 8 8

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. 9

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. p q r s LM 10

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. p q r s LM leader = r 11

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. p q r s IMIM IMIM IMIM wait 2D rounds 12

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 p q r s waiting 2D rounds LM leader = r 13

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 p q r s q:IM r:IM s:IM entered region the earliest candidate leader = r waiting 2D rounds LM leader = r p:IM wait for r’s leader msg 14

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. 15

16. Bounds Each node has a leader variable (node p’s leader variable : leader p ). Nodes elect the leader by setting the leader variable. (Termination) If some node p stays in the region for (6D-2)N e + D rounds it will elect itself as the leader assuming that no other node elected itself as the leader during this period (N e : number of nodes in the region when p entered the region) (Validity) If leader p = 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 leader p = q at round r 1 and leader p ≠ q at round r 2 where r 1 < r 2, then there exists a round in [r 1 -2D+1, r 2 ] where node q has either crashed or left the region. 16

17. A Condition on Mobility 17 δ : minimum progress C : communication radius S (v 0 ) δ C F v1v1 δ C F v1v1 region S (v 0 ) δ C F v1v1 region v2v2 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 = v 0, v 1,..., v k such that for all i : 0 ≤ i ≤ k-1 v i broadcasts at round r+i, v i and v i+1 are within communication radius of each other throughout r+i and when v i+1 broadcasts it lies within the shaded area of the figure, Position F is within the communication radius of v k

18. Calculation of D (1) Considering information propagation from S to F the worst case position of v 1 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. 18 δ : minimum progress C : communication radius S (v 0 ) δ C F A B

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 19 δ : minimum progress C : communication radius S (v 0 ) δ C F B F B P C δ δ : minimum progress C : communication radius G H C δ G δ C H L region G H L

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

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. 21

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. 22

23. Have a nice flight back home ! 23