An algorithm for optimal placement of sensor elements

The problem of finding the optimal minimum-redundancy integer locations for an array of given sensors that span a prescribed distance N, such that any missing integer i (0<i<N) is expressible as the difference of two sensor locations, is addressed; a greedy algorithm is presented. This problem is formulated from a number-theoretic point of view and the actual algorithm for optimal sensor placement is described together with a modified version which reduces the computation time and required memory storage. It is shown that these greedy algorithms are clearly suboptimal, since for a given M the maximum attainable value for N is found to be less than N_M