Improved approximation algorithms for minimum-space advertisement scheduling

Abstract

We study a scheduling problem involving the optimal placement of advertisement images in a shared space over time. The problem is a generalization of the classical scheduling problem P\\Cmax, and involves scheduling each job on a specified number of parallel machines (not necessarily simultaneously) with a goal of minimizing the makespan. In 1969 Graham showed that processing jobs in decreasing order of size, assigning each to the currently-least-loaded machine, yields a 4/3-approximation for P\\Cmax. Our main result is a proof that the natural generalization of Graham's algorithm also yields a 4/3-approximation to the minimumspace advertisement scheduling problem. Previously, this algorithm was only known to give an approximation ratio of 2, and the best known approximation ratio for any algorithm for the minimum-space ad scheduling problem was 3/2. Our proof requires a number of new structural insights, which leads to a new lower bound for the problem and a non-trivial linear programming relaxation. We also provide a pseudo-polynomial approximation scheme for the problem (polynomial in the size of the problem and the number of machines). © Springer-Verlag Berlin Heidelberg 2003.