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This paper describes the predetermined interaction list oct-tree (PILOT) algorithm and its application in expediting the solution of full-wave electric field integral equation (EFIE)-based scattering problems for three-dimensional arbitrarily shaped conductors. PILOT combines features of the fast multipole method (FMM) and QR decomposition-based matrix compression techniques to optimize setup times, solve times, and memory requirements. The method is kernel independent and stable for electrically small structures unlike traditional FMM. The novel features of the algorithm, namely the mixed potential compression scheme and the hierarchical multilevel predetermined matrix structure are explained in detail. A complexity estimate is presented to demonstrate the scaling in time and memory requirements. Examples exhibiting the accuracy and the time and memory performances are also presented. Finally, a quantitative study is included to address the expected but gradual degradation of QR-based compression techniques for electrically large structures.