Presenter: Nirav Shah

1. Max-Min D-Cluster Formation in Wireless Ad Hoc Networks- Alan Amis, Ravi Prakash, Thai Vuong, Dung Huynh Presenter: Nirav Shah

2. Agenda • Problem Statement • System Model • Earlier Design Choices • Max-Min Algorithm • Simulation Results • Conclusion

3. Problem Statement • Ad Hoc network needs efficient communication between nodes • Develop wireless backbone architecture • Clusterheads and Gateways • Backbone must be continuously reconstructed in a timely fashion • Previous algorithms of O(n) complexity (n = # of nodes) • Need for efficient algorithm for leader election for clusterheads • Complexity of O(d), d = a node that is d hops away from the leader

4. System Model • All nodes are alike and mobile in ad hoc networks • There are no base stations to coordinate the activities of subset of nodes • Max-Min heuristic only considers bidirectional links. MAC layer masks unidirectional links and pass bidirectional links to Max-Min • Beacons used to determine the presence of neighboring nodes • Communication between nodes is over a single shared channel • Node mobility results in neighborhood changes. Consequently, the topology changes as well

5. Earlier Design Choices • Have all nodes maintain knowledge of the network and manage themselves • Imposes significant communication responsibility on individual nodes • Number of messages needed to maintain routing tables cause congestion in the network • Huge delays in message propagation from one node to another • Identify subset of nodes and assign them as clusterheads to manage close proximity nodes. • Clusterheads manage communication between nodes in their neighborhood • Past solutions involved creating network where every node was no more than 1 hop away from a clusterhead. • Generate large number of clusterheads and eventually leading to above problem

6. Earlier Design Choices • Linked Cluster Algorithm • Communicate using TDMA frames • Requires 2n TDMA timeslots, where n is number of nodes • Intended for network of 100 nodes or less • Impose greater delays in node transmissions using TDMA as number of nodes increase significantly.

7. Objective: Max-Min Algorithm • To develop a heuristic that would elect multiple leaders in large ad hoc networks of thousands of nodes. • Collection of nodes that are up to d hops away from a clusterhead, where d >= 1. Also known as d-hop dominating set • Formation of d-hop dominating set is NP-complete problem. Forget the Proof  • Need for a heuristic to solve the problem

8. Design Goals: Max-Min Algorithm • Nodes asynchronously run the heuristic: no need for synchronized clocks • Limit the number of messages sent between nodes to O(d) • Minimize the number and size of the data structures required to implement the heuristic • Minimize the number of clusterheads as a function of d • Formation of backbone using gateways • Stability: Re-elect clusterheads when possible • Fairness: Distribute responsibility of managing clusters is equally distributed among all nodes

9. Data Structures: Max-Min Algorithm • Algorithm runs for 2d rounds of information exchange • Each node maintains 2 arrays, WINNER and SENDER, each of size 2d node ids • WINNER: winning node id of a particular round and used to determine the clusterhead for a node • SENDER: node that sent the winning node id for a particular round and is used to determine the shortest path back to the clusterhead, once the clusterhead is selected.

10. Steps: Max-Min Algorithm • Each node sets WINNER to be equal to its own node id. • FLOODMAX: Each node broadcasts WINNER value to 1-hop neighbors • The node selects largest value from its own WINNER value and WINNER values received from its neighbors • Repeat steps 2 and 3 for d rounds. • At the end of FloodMax round surviving node ids are selected as clusterheads • FloodMax is a greedy algorithm that results in unbalanced load for the clusterheads

11. Steps: Max-Min Algorithm • FLOODMIN: Same as FLOODMAX except that node selects smallest instead of largest value • Allows smaller clusterheads to regain nodes within their d-neighborhood • At the end of FloodMin, each node evaluates the round’s WINNERs to best determine their clusterhead • In case a node’s id is overtaken by larger node id, FloodMin will ensure fairness • Finally, gateway nodes establish the backbone network • Start convergecast messaging to link all nodes of cluster to clusterheads and link clusterhead to other clusters.

12. Simulation: Max-Min Algorithm

13. Complexity: Max-Min Algorithm • Message Complexity • 2d messages to elect clusterheads • d messages to initiate convergecast to inform clusterhead of its children • O(2d + d) • Space Complexity • 2d node ids in its WINNER data structure • 2d node ids in its SENDER data structure • i.e. O(2d + 2d)

14. Simulation Results: Max-Min Algorithm • Mean number of clusterheads in a network • Too many clusterheads - too few nodes being managed by each clusterhead • Too few clusterheads - too many nodes being managed by each clusterhead

15. Simulation Results: Max-Min Algorithm • Mean time for which once a node is elected as clusterhead, it stays as a clusterhead • The longer the duration, the more stable the system

16. Simulation Results: Max-Min Algorithm • Mean size of a cluster • Inversely proportional to the number of clusterheads • large clusters -> overloaded clusterheads • small clusters -> idle clusterheads

17. Conclusion • Max-Min runs asynchronously eliminating the need and overhead of highly synchronized clocks • Algorithm generalized for d hop distance allowing flexibility and control to determine clusterhead density • Scalable solution to generate small number of clusterheads compared to other heuristics • Forms redundant backbone architecture to provide better availability • Future work needed to determine the appropriate time to trigger Max-Min algorithm. • Periodic triggers closely spaced – very frequent message passing • Periodic triggers far apart – overlooks changing topology

18. Q & A