An FPTAS for Agreeably Weighted Variance on a Single Machine

Authors:
Gerhard J. Woeginger
Affiliations:
-
Venue:
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Year:
1999

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Abstract

We investigate the following scheduling problem: There is a single machine and a set of jobs. Every job is specified by its processing time and by its weight. The goal is to find a schedule that minimizes the sum of squared deviations from the weighted average job completion time. Jobs with small processing times have large weights, and hence the weights are agreeable. This problem is NP-hard. In 1995, Cai derived a fully polynomial time approximation scheme for the special case where the weights of the jobs are polynomially bounded in the number n of jobs. In this paper we completely settle the approximability status of this scheduling problem: We construct a fully polynomial time approximation scheme for the general case, without putting any restrictions on the weights of the jobs.