On Minimizing the Maximum Sensor Movement for Barrier Coverage of a Line Segment

We consider n mobile sensors located on a line containing a barrier represented by a finite line segment Sensors form a Wireless Sensor network and are able to move within the line An intruder traversing the barrier can be detected only when it is within the sensing range of at least one sensor The sensor network establishes barrier coverage of the segment if no intruder can penetrade the barrier from any direction in the plane without being detected Starting from arbitrary initial positions of sensors oil the line we are interested in finding final positions of sensors that establish barrier coverage and minimize the maximum distance traversed by any sensor We distinguish Several Variants of the problem, based on (a) whether or not the sensors have identical ranges (b) whether or not complete coverage is possible and (c) in the case when complete coverage is impossible, whether or not the maximal cover age is required to be contiguous For the owe or n sensors identical range, When complete coverage is impossible, we give linear tune optimal algorithms that achieve maximal coverage: both for the contigous and non-contigous case. when Complete coverage is possible, we give an O(n(2)) algorithin for an optimal solution a linear time approximation scheme with approximation factor 2 and a, (1 + c) PTAS When the sensors have unequal ranges we show that a variation of the problem is NP-complete and identify some instances Much can be solved will our algorithms for sensors with unequal ranges