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

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

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

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

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

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.

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

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

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.

Steps: Max-Min Algorithm 1. Each node sets WINNER to be equal to its own node id. 2. FLOODMAX: Each node broadcasts WINNER value to 1-hop neighbors 3. The node selects largest value from its own WINNER value and WINNER values received from its neighbors 4. Repeat steps 2 and 3 for d rounds. 5. At the end of FloodMax round surviving node ids are selected as clusterheads 6. FloodMax is a greedy algorithm that results in unbalanced load for the clusterheads

Steps: Max-Min Algorithm 7. FLOODMIN: Same as FLOODMAX except that node selects smallest instead of largest value Allows smaller clusterheads to regain nodes within their d- neighborhood 8. At the end of FloodMin, each node evaluates the round’s WINNERs to best determine their clusterhead 9. In case a node’s id is overtaken by larger node id, FloodMin will ensure fairness 10. Finally, gateway nodes establish the backbone network Start convergecast messaging to link all nodes of cluster to clusterheads and link clusterhead to other clusters.

Simulation: Max-Min Algorithm

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)

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

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

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

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

Q & A