1. Topology Control in Wireless Sensor Networks

2. 2 Three R&D Styles  Intuitive approach (e.g., directed diffusion)  Easy to understand, a lot of follow-up work  refreshing ideas make you happily surprised Need a BIG and innovative idea  Easy to attack since everyone can understand the work quickly  Analytical approach (e.g. this homework)  Solid work, summarizing or generalizing previous pieces of work  Novelty may be limited, practical impact??  System approach (e.g. the modular net layer paper)  Practical impact is HUGE  Insights learned from system building and user experiences  No new ideas that will blow your mind away A collection of small ideas or tricks

3. 3 Coverage and Connectivity  Problem Formulation  Maximize number of sleeping nodes so that convex region A is Ks covered and all active nodes are connected  Assumptions  Sensing and communication regions are circular  All nodes have same ranges, Rs and Rc Nodes can communicate if they are within Rc Nodes ensure sensing within Rs  Each node knows its location  Intuition: Ratio Rc/Rs is critical to coverage and connectivity

4. 4 Problem continued  Connectivity requirement: any active node must be within Rc of at least one other active node  Coverage requirement: all locations in the coverage region must be within Rs of at least one active node

5. 5 Problem continued  Coverage degree Ks and connectivity degree Kc  Can connectivity --> coverage? No, connectivity only cares about active nodes  Can coverage --> connectivity? Yes only if Rc >= 2Rs Theorem: a set of nodes that Ks-cover a convex region forms a Ks-connected communication graph if Rc >= 2Rs

6. 6 Coverage configuration protocol (CCP)  Configuration protocol based on Theorem above  Coverage --> connectivity when Rc >=2Rs  Can configure a network to a requested coverage degree  Decentralized protocol only requires local neighbor states to determine specific node states (eligibility rules)  All we need to do is to activate nodes to cover a region with a specified degree and we are connected!  Issues: how does a node know its sensing region is already covered?

7. 7 Sufficient condition for coverage  Theorem: a convex region A is Ks-covered if all intersection points between nodes, and between nodes and the region boundary are Ks-covered  Intuitively all points in same patch have same coverage degree  Only checking the intersection points

8. 8 Ks-coverage eligibility algorithm in CCP  A node is eligible to turn active if any intersection point inside its sensing circle is not already Ks-covered  steps  All nodes are active when deployed  Active nodes periodically broadcast/receive beacon messages  Sleeping nodes periodically wake up to receive these beacons and decide whether to stay waked up or not

9. 9 What about the case when Rc < 2Rs?  CCP is not sufficient as coverage will not lead to connectivity  Solution: combine a coverage protocol CCP with a connectivity protocol SPAN  What is SPAN? Connectivity-only protocol Eligibility rule: a sleeping node will be eligible to be active if a pair of neighbors are unable to reach each other directly or through one or two active nodes A sleeping node is within the communication range of an active node  Use both eligibility rules Activate if either CCP or SPAN’s eligibility rule is satisfied Sleep if neither is satisfied.  Hello beacons contain info about other active nodes