TY - GEN

T1 - Brief announcement

T2 - 28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016

AU - Katz, Dmitriy

AU - Schieber, Baruch

AU - Shachnai, Hadas

N1 - Funding Information:
This work was partly carried out during a visit to DIMACS supported by the National Science Foundation under grant number CCF-1144502.

PY - 2016/7/11

Y1 - 2016/7/11

N2 - Motivated by the cloud computing paradigm, and by key optimization problems in all-optical networks, we study two variants of the classic job interval scheduling problem, where a reusable resource is allocated to competing job intervals in a flexible manner. Each job, Ji, requires the use of up to rmax(i) units of the resource, with a profit of pi ≥ 1 accrued for each allocated unit. The goal is to feasibly schedule a subset of the jobs so as to maximize the total profit. The resource can be allocated either in contiguous or non-contiguous blocks. These problems can be viewed as flexible variants of the well known storage allocation and bandwidth allocation problems. We show that the contiguous version is strongly NP-hard, already for instances where all jobs have the same profit and the same maximum resource requirement. We derive the best possible positive result for such instances, namely, a polynomial time approximation scheme (PTAS). We further show that the contiguous variant admits a (5/4 + ϵ)-approximation algorithm, for any fixed ϵ > 0, on instances whose job intervals form a proper interval graph. At the heart of the algorithm lies a non-standard parameterization of the approximation ratio itself. For the noncontiguous case, we uncover an interesting relation to the paging problem that leads to a simple O(nlogn) algorithm for uniform profit instances of n jobs.

AB - Motivated by the cloud computing paradigm, and by key optimization problems in all-optical networks, we study two variants of the classic job interval scheduling problem, where a reusable resource is allocated to competing job intervals in a flexible manner. Each job, Ji, requires the use of up to rmax(i) units of the resource, with a profit of pi ≥ 1 accrued for each allocated unit. The goal is to feasibly schedule a subset of the jobs so as to maximize the total profit. The resource can be allocated either in contiguous or non-contiguous blocks. These problems can be viewed as flexible variants of the well known storage allocation and bandwidth allocation problems. We show that the contiguous version is strongly NP-hard, already for instances where all jobs have the same profit and the same maximum resource requirement. We derive the best possible positive result for such instances, namely, a polynomial time approximation scheme (PTAS). We further show that the contiguous variant admits a (5/4 + ϵ)-approximation algorithm, for any fixed ϵ > 0, on instances whose job intervals form a proper interval graph. At the heart of the algorithm lies a non-standard parameterization of the approximation ratio itself. For the noncontiguous case, we uncover an interesting relation to the paging problem that leads to a simple O(nlogn) algorithm for uniform profit instances of n jobs.

KW - Bandwidth allocation

KW - Cloud computing

KW - Flexgrid all-optical networks

KW - Flexible storage allocation

KW - Paging

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=84979780632&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979780632&partnerID=8YFLogxK

U2 - 10.1145/2935764.2935806

DO - 10.1145/2935764.2935806

M3 - Conference contribution

AN - SCOPUS:84979780632

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 225

EP - 226

BT - SPAA 2016 - Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

PB - Association for Computing Machinery

Y2 - 11 July 2016 through 13 July 2016

ER -