Approximation algorithms for the job interval selection problem and related scheduling problems

The authors consider the job interval selection problem (JISP), a simple scheduling model with a rich history and numerous applications. Special cases of this problem include the so-called real-time scheduling problem (also known as the throughput maximization problem) in single and multiple machine environments. In these special cases we have to maximize the number of jobs scheduled between their release date and deadline (preemption is not allowed). Even the single machine case is NP-hard. The unrelated machines case, as well as other special cases of JISP, are MAX SNP-hard. A simple greedy algorithm gives a 2-approximation for JISP. Despite many efforts, this was the best approximation guarantee known, even for throughput maximization on a single machine. The authors break this barrier and show an approximation guarantee of less than 1.582 for arbitrary instances of JISP. For some special cases, we show better results. Our methods can be used to give improved bounds for some related resource allocation problems that were considered recently in the literature.

[1]  Philippe Baptiste,et al.  Polynomial time algorithms for minimizing the weighted number of late jobs on a single machine with equal processing times , 1999 .

[2]  Toshihide Ibaraki,et al.  A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times , 1978, Oper. Res..

[3]  F. Spieksma.  On the approximability of an interval scheduling problem , 1999 .

[4]  O. E. Flippo,et al.  The assembly of printed circuit boards : a case with multiple machines and multiple board types , 1995 .

[5]  Hang Liu,et al.  Adaptive source rate control for real‐time wireless video transmission , 1998, Mob. Networks Appl..

[6]  N. S. Barnett,et al.  Private communication , 1969 .

[7]  P. Berman,et al.  Improvements in Throughput Maximization for Real-Time Scheduling , 1999 .

[8]  Piotr Berman,et al.  Improvements in throughout maximization for real-time scheduling , 2000, STOC '00.

[9]  Sudipto Guha,et al.  Approximating the Throughput of Multiple Machines in Real-Time Scheduling , 2002, SIAM J. Comput..

[10]  Arnold L. Rosenberg,et al.  Scheduling Time-Constrained Communication in Linear Networks , 1998, SPAA.

[11]  Richard J. Lipton,et al.  Online interval scheduling , 1994, SODA '94.

[12]  Reuven Bar-Yehuda,et al.  A unified approach to approximating resource allocation and scheduling , 2000, STOC '00.

[13]  Esther M. Arkin,et al.  Scheduling jobs with fixed start and end times , 1987, Discret. Appl. Math..

[14]  J. M. Moore.  An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[15]  Ulrich Faigle,et al.  Note on Scheduling Intervals on-line , 1995, Discret. Appl. Math..

[16]  Nicholas G. Hall,et al.  Maximizing the value of a space mission , 1994 .

[17]  Sudipto Guha,et al.  Approximating the throughput of multiple machines under real-time scheduling , 1999, STOC '99.

[18]  Matteo Fischetti,et al.  The Fixed Job Schedule Problem with Spread-Time Constraints , 1987, Oper. Res..

[19]  Yuval Rabani,et al.  Improved Approximation Algorithms for Resource Allocation , 2002, IPCO.

[20]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.

[21]  Dennis Shasha,et al.  D^over: An Optimal On-Line Scheduling Algorithm for Overloaded Uniprocessor Real-Time Systems , 1995, SIAM J. Comput..

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

[23]  Dennis Shasha,et al.  D/sup over/; an optimal on-line scheduling algorithm for overloaded real-time systems , 1992, [1992] Proceedings Real-Time Systems Symposium.

[24]  David S. Johnson,et al.  Two-Processor Scheduling with Start-Times and Deadlines , 1977, SIAM J. Comput..

[25]  Roshdy H. M. Hafez,et al.  Adaptive rate controlled, robust video communication over packet wireless networks , 1998, Mob. Networks Appl..

[26]  David K. Y. Yau,et al.  Adaptive rate-controlled scheduling for multimedia applications , 1997, TNET.

[27]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .