Brooks–Iyengar algorithm

The Brooks–Iyengar algorithm or Brooks–Iyengar hybrid algorithm is a distributed algorithm that improves both the precision and accuracy of the interval measurements taken by a distributed sensor network, even in the presence of faulty sensors. The sensor network does this by exchanging the measured value and accuracy value at every node with every other node, and computes the accuracy range and a measured value for the whole network from all of the values collected. Even if some of the data from some of the sensors is faulty, the sensor network will not malfunction. The algorithm is fault-tolerant and distributed. It could also be used as a sensor fusion method. The precision and accuracy bound of this algorithm have been proved in 2016. The Brooks–Iyengar algorithm or Brooks–Iyengar hybrid algorithm is a distributed algorithm that improves both the precision and accuracy of the interval measurements taken by a distributed sensor network, even in the presence of faulty sensors. The sensor network does this by exchanging the measured value and accuracy value at every node with every other node, and computes the accuracy range and a measured value for the whole network from all of the values collected. Even if some of the data from some of the sensors is faulty, the sensor network will not malfunction. The algorithm is fault-tolerant and distributed. It could also be used as a sensor fusion method. The precision and accuracy bound of this algorithm have been proved in 2016. The Brooks–Iyengar hybrid algorithm for distributed control in the presence of noisy data combines Byzantine agreement with sensor fusion. It bridges the gap between sensor fusion and Byzantine fault tolerance. This seminal algorithm unified these disparate fields for the first time. Essentially, it combines Dolev’s algorithm for approximate agreement with Mahaney and Schneider’s fast convergence algorithm (FCA). The algorithm assumes N processing elements (PEs), t of which are faulty and can behave maliciously. It takes as input either real values with inherent inaccuracy or noise (which can be unknown), or a real value with apriori defined uncertainty, or an interval. The output of the algorithm is a real value with an explicitly specified accuracy. The algorithm runs in O(NlogN) where N is the number of PEs: see Big O notation. It is possible to modify this algorithm to correspond to Crusader’s Convergence Algorithm (CCA), however, the bandwidth requirement will also increase. The algorithm has applications in distributed control, software reliability, High-performance computing, etc. The Brooks–Iyengar algorithm is executed in every processing element (PE) of a distributed sensor network. Each PE exchanges their measured interval with all other PEs in the network. The 'fused' measurement is a weighted average of the midpoints of the regions found. The concrete steps of Brooks–Iyengar algorithm are shown in this section. Each PE performs the algorithm separately: Input: The measurement sent by PE k to PE i is a closed interval [ l k , i , h k , i ] {displaystyle } , 1 ≤ k ≤ N {displaystyle 1leq kleq N} Output: The output of PE i includes a point estimate and an interval estimate Example: Consider an example of 5 PEs, in which PE 5 ( S 5 {displaystyle S_{5}} ) is sending wrong values to other PEs and they all exchange the values.