Flexible Resource Allocation to Interval Jobs

• Published in: Algorithmica Vol. 81; no. 8; pp. 3217 - 3244
• Main Authors: Katz, Dmitriy, Schieber, Baruch, Shachnai, Hadas
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2019; Springer Nature B.V
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Approximation; Cloud computing; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Intervals; Mathematical analysis; Mathematics of Computing; Optical communication; Optimization; Paging; Parameterization; Polynomials; Production scheduling; Resource allocation; Schedules; Theory of Computation; Cloud computing; Flexible storage allocation; Approximation algorithms; Scheduling; Bandwidth allocation; Elastic all-optical networks; Paging problem
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-019-00582-9

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, J i , requires the use of up to r max ( i ) units of the resource, with a profit of p i ≥ 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. For such instances, we derive the best possible positive result, namely, a polynomial time approximation scheme. 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, which is of independent interest. For the non-contiguous case, we uncover an interesting relation to the paging problem that leads to a simple O ( n log n ) algorithm for uniform profit instances of n jobs. The algorithm is easy to implement and is thus practical.