Approximability and Nonapproximability Results for Minimizing Total Flow Time on a Single Machine

We consider the problem of scheduling n jobs that are released over time on a single machine in order to minimize the total ow time. This problem is well-known to be NPcomplete, and the best polynomial time approximation algorithms constructed so far had (more or less trivial) worst-case performance guarantees of O(n). In this paper, we present one positive and one negative result on polynomial time approximations for the minimumtotal ow time problem: The positive result is the rst approximation algorithm with a sublinear worst-case performance guarantee of O( p n). This algorithm is based on resolving the preemptions of the corresponding optimum preemptive schedule. The performance guarantee of our approximation algorithm is not far from best possible as our second, negative, result demonstrates: Unless P = NP , no polynomial time approximation algorithm for minimum total ow time can have a worst-case performance guarantee of O(n 1 2 ;") for any " > 0.

• Type: Conference
• Year: 1996
• Where: STOC
• Authors: Hans Kellerer, Thomas Tautenhahn, Gerhard J. Woeginger
• Keywords: Algorithms, Approximation Algorithm, Polynomial Time Approximation, STOC 1996, Worst-case Performance Guarantee