## Abstract

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 (54+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(nlog n) algorithm for uniform profit instances of n jobs. The algorithm is easy to implement and is thus practical.

Original language | English (US) |
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Pages (from-to) | 3217-3244 |

Number of pages | 28 |

Journal | Algorithmica |

Volume | 81 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2019 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Computer Science
- Computer Science Applications
- Applied Mathematics

## Keywords

- Approximation algorithms
- Bandwidth allocation
- Cloud computing
- Elastic all-optical networks
- Flexible storage allocation
- Paging problem
- Scheduling