Grouping Techniques for Scheduling Problems: Simpler and Faster

In this paper we describe a general grouping technique to devise faster and simpler approximation schemes for several scheduling problems. We illustrate the technique on two different scheduling problems: scheduling on unrelated parallel machines with costs and the job shop scheduling problem. The time complexity of the resulting approximation schemes is always linear in the number n of jobs, and the multiplicative constant hidden in the O(n) running time is reasonably small and independent of the error Ɛ.

[1]  Klaus Jansen,et al.  Makespan minimization in job shops: a polynomial time approximation scheme , 1999, STOC '99.

[2]  Leonid Khachiyan,et al.  Coordination Complexity of Parallel Price-Directive Decomposition , 1996, Math. Oper. Res..

[3]  Gerhard J. Woeginger,et al.  Approximation schemes-a tutorial , 2001 .

[4]  Jianer Chen,et al.  A Polynomial Time Approximation Scheme for General Multiprocessor Job Scheduling , 2001, SIAM J. Comput..

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

[6]  Klaus Jansen,et al.  Polynomial time approximation schemes for general multiprocessor job shop scheduling , 2002, J. Algorithms.

[7]  Sergey Vasil'evich Sevast'janov,et al.  on Some Geometric Methods in Scheduling Theory: A Survey , 1994, Discret. Appl. Math..

[8]  Monaldo Mastrolilli,et al.  Efficient Approximation Schemes for Scheduling Problems with Release Dates and Delivery Times , 2003, J. Sched..

[9]  Evripidis Bampis,et al.  Approximation schemes for minimizing average weighted completion time with release dates , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[10]  L. Goddard,et al.  Operations Research (OR) , 2007 .

[11]  Jianer Chen,et al.  A polynomial time approximation scheme for general multiprocessor job scheduling (extended abstract) , 1999, STOC '99.

[12]  David B. Shmoys,et al.  Improved approximation algorithms for shop scheduling problems , 1991, SODA '91.

[13]  Klaus Jansen,et al.  A Linear Time Approximation Scheme for the Job Shop Scheduling Problem , 1999, RANDOM-APPROX.

[14]  Evripidis Bampis,et al.  Scheduling Independent Multiprocessor Tasks , 2002, Algorithmica.

[15]  Klaus Jansen,et al.  Polynominal Time Approximation Schemes for General Multiprocessor Job Shop Scheduling , 2000, ICALP.

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

[17]  Aravind Srinivasan,et al.  Better approximation guarantees for job-shop scheduling , 1997, SODA '97.

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

[19]  Klaus Jansen,et al.  Improved approximation schemes for scheduling unrelated parallel machines , 1999, STOC '99.

[20]  Gerhard J. Woeginger,et al.  Makespan minimization in open shops: A polynomial time approximation scheme , 1998, Math. Program..

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

[22]  Ellis Horowitz,et al.  Exact and Approximate Algorithms for Scheduling Nonidentical Processors , 1976, JACM.

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

[24]  Éva Tardos,et al.  An approximation algorithm for the generalized assignment problem , 1993, Math. Program..

[25]  Leslie A. Hall.  Approximability of flow shop scheduling , 1998, Math. Program..

[26]  David B. Shmoys,et al.  Near-Optimal Sequencing with Precedence Constraints , 1990, IPCO.

[27]  Klaus Jansen,et al.  Linear-Time Approximation Schemes for Scheduling Malleable Parallel Tasks , 1999, SODA '99.

[28]  Klaus Jansen,et al.  Makespan Minimization in Job Shops: A Linear Time Approximation Scheme , 2003, SIAM J. Discret. Math..