Set It and Forget It: Approximating the Set Once Strip Cover Problem

We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard. Second, we show that RoundRobin, the algorithm in which the sensors simply take turns covering the entire region, has a tight approximation guarantee of 3/2 in both Set Once Strip Cover and the more general Strip Cover problem, in which each radius may be set finitely-many times. Moreover, we show that the more general class of duty cycle algorithms, in which groups of sensors take turns covering the entire region, can do no better. Finally, we give an optimal O(n^2 log n)-time algorithm for the related Set Radius Strip Cover problem, in which all sensors must be activated immediately.Comment: briefly announced at SPAA 201

Average Case Network Lifetime on an Interval with Adjustable Sensing Ranges

Given n sensors on an interval, each of which is equipped with an adjustable sensing radius and a unit battery charge that drains in inverse linear proportion to its radius, what schedule will maximize the lifetime of a network that covers the entire interval? Trivially, any reasonable algorithm is at least a 2-approximation for this Sensor Strip Cover problem, so we focus on developing an efficient algorithm that maximizes the expected network lifetime under a random uniform model of sensor distribution. We demonstrate one such algorithm that achieves an expected network lifetime within 12 % of the theoretical maximum. Most of the algorithms that we consider come from a particular family of RoundRobin coverage, in which sensors take turns covering predefined areas until their battery runs out

Maximizing Network Lifetime on the Line with Adjustable Sensing Ranges

Given n sensors on a line, each of which is equipped with a unit battery charge and an adjustable sensing radius, what schedule will maximize the lifetime of a network that covers the entire line? Trivially, any reasonable algorithm is at least a 1/2-approximation, but we prove tighter bounds for several natural algorithms. We focus on developing a linear time algorithm that maximizes the expected lifetime under a random uniform model of sensor distribution. We demonstrate one such algorithm that achieves an average-case approximation ratio of almost 0.9. Most of the algorithms that we consider come from a family based on RoundRobin coverage, in which sensors take turns covering predefined areas until their battery runs out

Lean, Green, and Lifetime Maximizing Sensor Deployment on a Barrier

Mobile sensors are located on a barrier represented by a line segment, and each sensor has a single energy source that can be used for both moving and sensing. Sensors may move once to their desired destinations and then coverage/communication is commenced. The sensors are collectively required to cover the barrier or in the communication scenario set up a chain of communication from endpoint to endpoint. A sensor consumes energy in movement in proportion to distance traveled, and it expends energy per time unit for sensing in direct proportion to its radius raised to a constant exponent. The first focus is of energy efficient coverage. A solution is sought which minimizes the sum of energy expended by all sensors while guaranteeing coverage for a predetermined amount of time. The objective of minimizing the maximum energy expended by any one sensor is also considered. The dual model is then studied. Sensors are equipped with batteries and a solution is sought which maximizes the coverage lifetime of the network, i.e. the minimum lifetime of any sensor. In both of these models, the variant where sensors are equipped with predetermined radii is also examined. Lastly, the problem of maximizing the lifetime of a wireless connection between a transmitter and a receiver using mobile relays is considered. These problems are mainly examined from the point of view of approximation algorithms due to the hardness of many of them