Maximizing total tardiness on a single machine in $$O(n^2)$$ O ( n 2 ) time via a reduction to half-product minimization

Abstract

Gafarov et al. (Ann Oper Res 196(1):247-261, 2012) have recently presented an O(n 2 ) time dynamic programming algorithm for a single machine scheduling problem to maximize the total job tardiness. We reduce this problem in O(n log n) time to a problem of unconstrained minimization of a function of 0-1 variables, called half-product, for which a simple O(n 2 ) time dynamic programming algorithm is known in the literature.