Parallel Algorithms That Locate Local Extrema of a Function of One Variable From Interval Measurement Results

The problem of locating local maxima and minima of a function from approximate measurement results is vital for many physical applications: in spectral analysis, chemical species are identified by locating local maxima of the spectra; in radioastronomy, sources of celestial radio emission and and their subcomponents are identified by locating local maxima of the measured brightness of the radio sky; elementary particles are identified by locating local maxima of the experimental curves. In [17], a sequential algorithm was proposed that solves this problem in linear time (i.e., in time ≤ Cn, where n is the number of measurements and C is a constant that is independent on n). In this paper, we propose parallel algorithms that find local maxima and minima in polylog time (≤ C log(n) on n processors, and ≤ C log(n) on n processors).