Non-approximability Results for Scheduling Problems with Minsum Criteria

We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless P = NP, none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by Max SNP hardness proofs. Among the investigated problems are: scheduling unrelated machines with some additional features like job release dates, deadlines and weights, scheduling flow shops, and scheduling open shops.

[1]  Han Hoogeveen,et al.  Three, four, five, six, or the complexity of scheduling with communication delays , 1994, Oper. Res. Lett..

[2]  Pierluigi Crescenzi,et al.  Approximation on the Web: A Compendium of NP Optimization Problems , 1997, RANDOM.

[3]  Gerhard J. Woeginger,et al.  Approximability and nonapproximability results for minimizing total flow time on a single machine , 1996, STOC '96.

[4]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[5]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[6]  Maurice Queyranne,et al.  Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems , 1998, IPCO.

[7]  Stefano Leonardi,et al.  Approximating total flow time on parallel machines , 1997, STOC '97.

[8]  Gerhard J. Woeginger,et al.  A PTAS for minimizing the weighted sum of job completion times on parallel machines , 1999, STOC '99.

[9]  David B. Shmoys,et al.  Scheduling to minimize average completion time: off-line and on-line algorithms , 1996, SODA '96.

[10]  Edward G. Coffman,et al.  Scheduling independent tasks to reduce mean finishing time , 1974, CACM.

[11]  Jan Karel Lenstra,et al.  Complexity of Scheduling under Precedence Constraints , 1978, Oper. Res..

[12]  Giorgio Gambosi,et al.  Complexity and Approximation , 1999, Springer Berlin Heidelberg.

[13]  Viggo Kann,et al.  Maximum Bounded 3-Dimensional Matching is MAX SNP-Complete , 1991, Inf. Process. Lett..

[14]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[15]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[16]  Martin Skutella,et al.  Random-Based Scheduling: New Approximations and LP Lower Bounds , 1997, RANDOM.

[17]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[18]  Eugene L. Lawler,et al.  Chapter 9 Sequencing and scheduling: Algorithms and complexity , 1993, Logistics of Production and Inventory.

[19]  Jan Karel Lenstra,et al.  Computing near-optimal schedules , 1995 .

[20]  Han Hoogeveen,et al.  Short Shop Schedules , 1997, Oper. Res..

[21]  Jan Karel Lenstra,et al.  Approximation algorithms for scheduling unrelated parallel machines , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).