Needle in a cross-layer sensor stack

In this problem, the process start with real-valued inputs and are supposed to decide eventually on real-valued outputs. The process is permitted to send real-valued data in messages. Instead of having to agree exactly, as in the ordinary agreement problem, this time the requirement is just that they agree with within a small positive real-valued tolerance ε. In the standard implementation agreement problem converges to a consistent value for each sensor measurement, which is nonfaculty using Byzantine algorithm with at-least n >; 3 faulty sensors. We define a pre-processing BestBasis cost function which allows to find a coherent range, which can be measured using intra-sensor in an ensemble of real-values. The overlap of the range is calculated by using a clique, with a runtime of O(nk) in the worst-case, where the size of clique, k, is a variable. The computation of the pre-processing takes O log(D), where D is the number of levels in a sparse signal basis. Which are some times analogously compared to needle in a hay stack definition.