Minimal sensor integrity in sensor grids

Given the increasing importance of optimal sensor deployment for battlefield strategists, the converse problem of reacting to a particular deployment by an enemy is equally significant and not yet addressed in a quantifiable manner in the literature. We address this issue by modeling a two stage game in which the opponent deploys sensors to cover a sensor field and we attempt to maximally reduce his coverage at minimal cost. In this context, we introduce the concept of minimal sensor integrity which measures the vulnerability of any sensor deployment. We find the best response by quantifying the merits of each response. While the problem of optimally deploying sensors subject to coverage constraints is NP-Complete, in this paper we show that the best response (i.e. the maximum vulnerability) can be computed in polynomial time for sensors with arbitrary coverage capabilities deployed over points in any dimensional space. In the special case when sensor coverages form an interval graph (as in a linear grid), we describe a better O(Min(M².NM)) dynamic programming algorithm.