Fast Algorithms for the Maximum Convolution Problem (abstract)

We describe two algorithms for solving the maximum convolution problem, i.e. the calculation of
c_k := max { a_{k-i} + b_i | 0 =< i <= n-1 }  for all k
with respect to given sequences (a_0,...,a_{n-1}), (b_0,...,b_{n-1}) of real numbers. Our first algorithm with expected running time O(n log n) is mainly of theoretical interest while our second algorithm allows a simpler, more practicable implementation and showed quite fast performance in numerical experiments.

Keywords: maximum convolution; probabilistic analysis


M.Bussieck@tu-bs.de
Nov 11 1993