The Price of Bounded Preemption
Authors: 
Noga Alon, Yossi Azar, Mark BerlinAuthors Info & Claims
Noga Alon, Yossi Azar, Mark BerlinAuthors Info & ClaimsArticle No.: 3, Pages 1 - 21
Abstract
In this article we provide a tight bound for the price of preemption for scheduling jobs on a single machine (or multiple machines). The input consists of a set of jobs to be scheduled and of an integer parameter k ≥ 1. Each job has a release time, deadline, length (also called processing time), and value associated with it. The goal is to feasibly schedule a subset of the jobs so that their total value is maximal; while preemption of a job is permitted, a job may be preempted no more than k times. The price of preemption is the worst possible (i.e., largest) ratio of the optimal non-bounded-preemptive scheduling to the optimal k-bounded-preemptive scheduling.
Our results show that allowing at most k preemptions suffices to guarantee a Θ(min {logk+1 n, logk+1P}) fraction of the total value achieved when the number of preemptions is unrestricted (where n is the number of the jobs and P the ratio of the maximal length to the minimal length), giving us an upper bound for the price; a specific scenario serves to prove the tightness of this bound. We further show that when no preemptions are permitted at all (i.e., k=0), the price is Θ (min {n, log P}).
As part of the proof, we introduce the notion of the Bounded-Degree Ancestor-Free Sub-Forest (BAS). We investigate the problem of computing the maximal-value BAS of a given forest and give a tight bound for the loss factor, which is Θ(logk+1 n) as well, where n is the size of the original forest and k is the bound on the degree of the sub-forest.
References
[1]
Sivan Albagli-Kim, Baruch Schieber, Hadas Shachnai, and Tami Tamir. 2016. Real-time k-bounded preemptive scheduling. In Proceedings of the 18th Workshop on Algorithm Engineering and Experiments (ALENEX’16). 127--137.
[2]
Baruch Awerbuch, Yossi Azar, Amos Fiat, Stefano Leonardi, and Adi Rosén. 2001. On-line competitive algorithms for call admission in optical networks. Algorithmica 31, 1 (2001), 29--43.
[3]
Yossi Azar and Oren Gilon. 2017. Scheduling with deadlines and buffer management with processing requirements. Algorithmica 78, 4 (2017), 1246--1262.
[4]
Yossi Azar and Oded Regev. 2006. Combinatorial algorithms for the unsplittable flow problem. Algorithmica 44, 1 (2006), 49--66.
[5]
Philippe Baptiste. 1999. Polynomial time algorithms for minimizing the weighted number of late jobs on a single machine with equal processing times. Journal of Scheduling 2 (1999), 245--252.
[6]
Philippe Baptiste, Marek Chrobak, Christoph Dürr, Wojciech Jawor, and Nodari Vakhania. 2004. Preemptive scheduling of equal-length jobs to maximize weighted throughput. Operations Research Letters 32, 3 (2004), 258--264.
[7]
Amotz Bar-Noy, Reuven Bar-Yehuda, Ari Freund, Joseph Naor, and Baruch Schieber. 2001. A unified approach to approximating resource allocation and scheduling. Journal of the ACM 48, 5 (2001), 1069--1090.
[8]
Amotz Bar-Noy, Sudipto Guha, Joseph Naor, and Baruch Schieber. 2001. Approximating the throughput of multiple machines in real-time scheduling. SIAM Journal on Computing 31, 2 (2001), 331--352.
[9]
Reuven Bar-Yehuda and Shimon Even. 1985. A local ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics 25 (1985), 27--46.
[10]
Reuven Bar-Yehuda, Magnús M. Halldórsson, Joseph Naor, Hadas Shachnai, and Irina Shapira. 2006. Scheduling split intervals. SIAM Journal on Computing 36, 1 (2006), 1--15.
[11]
Sanjoy Baruah. 2005. The limited-preemption uniprocessor scheduling of sporadic task systems. In Proceedings of the 17th Euromicro Conference on Real-Time Systems (ECRTS’05). 137--144.
[12]
Reinder J. Bril, Johan J. Lukkien, and Wim F. J. Verhaegh. 2007. Worst-case response time analysis of real-time tasks under fixed-priority scheduling with deferred preemption revisited. In Proceedings of the 19th Euromicro Conference on Real-Time Systems (ECRTS’07). 269--279.
[13]
Giorgio C. Buttazzo, Marko Bertogna, and Gang Yao. 2013. Limited preemptive scheduling for real-time systems. a survey. IEEE Transactions on Industrial Informatics 9, 1 (2013), 3--15.
[14]
Ran Canetti and Sandy Irani. 1998. Bounding the power of preemption in randomized scheduling. SIAM Journal on Computing 27, 4 (1998), 993--1015.
[15]
Stéphane Dauzère-Pérès. 1995. Minimizing late jobs in the general one machine scheduling problem. European Journal of Operational Research 81, 1 (1995), 134--142.
[16]
Leah Epstein, Asaf Levin, Alan J. Soper, and Vitaly A. Strusevich. 2017. Power of preemption for minimizing total completion time on uniform parallel machines. SIAM Journal on Discrete Mathematics 31, 1 (2017), 101--123.
[17]
Ronald L. Graham, Eugene L. Lawler, Jan Karel Lenstra, and Alexander H. G. Rinnooy Kan. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 5 (1979), 287--326.
[18]
Bala Kalyanasundaram and Kirk Pruhs. 2001. Eliminating migration in multi-processor scheduling. Journal of Algorithms 38, 1 (2001), 2--24.
[19]
Richard M. Karp. 1972. Reducibility among combinatorial problems. In Complexity of Computer Computations, R. E. Miller and J. W. Thatcher (Eds.). Plenum Press, New York, 85--103.
[20]
Eugene L. Lawler. 1976. Sequencing to minimize the weighted number of tardy jobs. Rev. Française d’Automatique, Informatique, Recherche Opérationnel 10 (05 1976), 27--33.
[21]
Eugene L. Lawler. 1990. A dynamic programming algorithm for preemptive scheduling of a single machine to minimize the number of late jobs. Annals of Operations Research 26 (1990), 125--133.
[22]
Eugene L. Lawler. 1994. Knapsack-like scheduling problems, the Moore-Hodgson algorithm and the “tower of Sets” property. Mathematical and Computer Modelling 20, 2 (1994), 91--106.
[23]
Eugene L. Lawler and J. Michael Moore. 1969. A functional equation and its application to resource allocation and sequencing problems. Management Science 16 (1969), 77--84.
[24]
J. Michael Moore. 1968. Sequencing n jobs on one machine to minimize the number of tardy jobs. Management Science 15 (1968), 102--109.
[25]
Kirk Pruhs and Gerhard J. Woeginger. 2007. Approximation schemes for a class of subset selection problems. Theoretical Computer Science 382 (2007), 151--156.
[26]
Alan J. Soper and Vitaly A. Strusevich. 2014. Power of preemption on uniform parallel machines. Leibniz International Proceedings in Informatics (LIPIcs) 28 (2014), 392--402.
[27]
Yun Wang and Manas Saksena. 1999. Scheduling fixed-priority tasks with preemption threshold. In Proceedings of the 6th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA’99). 328--335.
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March 2021
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Publication History
Published: 18 March 2021
Accepted: 01 February 2020
Received: 01 April 2019
Published in TOPC Volume 8, Issue 1
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