Minimizing Profligacy of Searches with Reset

This submission contains associated materials (as two .zip files) relevant to the paper "Minimizing Profligacy of Searches with Reset." The materials include Julia programs for computing phase diagrams and Mathematica notebooks detailing calculations for Landau-like expansion. (i) Julia Programs: The Julia programs compute the the optimal value of resetting rate which minizmizes the profligacy of the search process and also computes the phase diagrams as obtained in the paper. These programs calculate the resetting rate that minimizes profligacy by scanning over a range of values for R, λ, and m in discrete steps. The programs compute transitions in the systems as parameters vary and classify them as continuous or discontinuous. The Julia programs utilize the Euler inversion algorithm, as described in "A Unified Framework for Numerically Inverting Laplace Transforms" by J. Abate and W. Whitt (INFORMS Journal on Computing, 2006) to numerically compute the inverse Laplace transform for the probability of success. gnuplot files and data used for generating figures in the paper are also provided. (ii) Mathematica Notebooks: The Mathematica notebook contains the detailed calculation for the Landau-like expansion performed in the supplemental materials for the paper.