Minimum-cost sensor coverage of planar regions

We consider the placement of sensors with circular sensing regions for q-coverage of planar regions.We first consider the placement of sensors of multiple types and costs over a specified set of locations to minimize the total sensorspsila cost. We present two approximate solutions to this problem with multiplicative factors of 3 and 1+1/l of the optimal cost, where l is a tunable parameter. We then present a method to transform a region coverage instance into an equivalent point coverage instance and show a relationship between the cost of the optimal coverage of the two instances. This transformation enables us to use better studied approximation algorithms for point coverage to derive good sensor deployments for region coverage.