The Profound Impact of the Brooks–Iyengar Algorithm

Abstract

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 a priori defined uncertainty, or an interval. The output of the algorithm is a real value with an explicitly specified accuracy. The algorithm runs in \(O(N\log N)\) and can be modified to correspond to Crusader’s Convergence Algorithm (CCA); however, the bandwidth requirement will also increase. The algorithm has applications in different fields from distributed control, software reliability, and High-performance computing. Motivated by the profound impact of this algorithm, the DARPA agency Sense-IT system used the Brooks–Iyengar fusion approach to combine sensor readings in real-time. Acoustic, seismic, and motion detection readings from multiple sensors were combined and fed into a distributed tracking system. This work was an essential precursor to the Emergent Sensor Plexus MURI from the Penn State Applied Research Laboratory (PSU/ARL). Following this demonstration, a number of other groups effectively deployed the algorithm in this product. For example, the Thales Group, a UK Defense Manufacturer, used this work as part of its Global Operational Analysis Laboratory. This chapter discusses the impact of Brooks–Iyengar algorithm on DARPA’s program, real-time UNIX systems, industrial companies like Raytheon and Telcordia, and academic theses/dissertations. It also addresses the algorithm potentials for future market growth.