TY - GEN

T1 - The price of bounded preemption

AU - Alon, Noga

AU - Azar, Yossi

AU - Berlin, Mark

PY - 2018/7/11

Y1 - 2018/7/11

N2 - In this paper 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+1 P}) 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.

AB - In this paper 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+1 P}) 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.

KW - Bounded preemptions

KW - Bounded-degree sub-forest

KW - Multiple machines

KW - Scheduling jobs

UR - http://www.scopus.com/inward/record.url?scp=85053485178&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053485178&partnerID=8YFLogxK

U2 - 10.1145/3210377.3210407

DO - 10.1145/3210377.3210407

M3 - Conference contribution

AN - SCOPUS:85053485178

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 301

EP - 310

BT - SPAA 2018 - Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures

PB - Association for Computing Machinery

T2 - 30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2018

Y2 - 16 July 2018 through 18 July 2018

ER -