Rounding of Sequences and Matrices, with Applications

Abstract. We show that any real matrix can be rounded to an integer matrix in such a way that the rounding errors of all row sums are less than one, and the rounding errors of all column sums as well as all sums of consecutive row entries are less than two. Such roundings can be computed in linear time. This extends and improves previous results on rounding sequences and matrices in several directions. It has particular applications in just-in-time scheduling, where balanced schedules on machines with negligible switch over costs are sought after. Here we extend existing results to multiple machines and non-constant production rates.

• Type: Conference
• Year: 2005
• Where: WAOA
• Authors: Benjamin Doerr, Tobias Friedrich, Christian Klein, Ralf Osbild
• Keywords: Consecutive Row Entries, Rounding Errors, Sums, WAOA 2005