Fully-polynomial Time Approximation Research Articles

Virtual Machine Migration Planning in Software-Defined Networks

In this paper, we examine the problem of how to schedule the migrations and how to allocate network resources for migration when multiple VMs need to be migrated at the same time. We consider the problem in the Software-defined Network (SDN) context since it provides flexible control on routing. More specifically, we propose a method that computes the optimal migration sequence and network bandwidth used for each migration. We formulate this problem as a mixed integer programming, which is NP-hard. To make it computationally feasible for large scale data centers, we propose an approximation scheme via linear approximation plus fully polynomial time approximation, and obtain its theoretical performance bound. Through extensive simulations, we demonstrate that our fully polynomial time approximation (FPTA) algorithm has a good performance compared with the optimal solution and two state of-the-art algorithms. That is, our proposed FPTA algorithm approaches to the optimal solution with less than 10% variation and much less computation time. Meanwhile, it reduces the total migration time and the service downtime by up to 40% and 20% compared with the state-of-the-art algorithms, respectively.

Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines

We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.

Computational performances of a simple interchange heuristic for a scheduling problem with an availability constraint

This paper deals with a scheduling problem on a single machine with an availability constraint. The problem is known to be NP-complete and admits several approximation algorithms. In this paper we study the approximation scheme described in He et al. [Y. He, W. Zhong, H. Gu, Improved algorithms for two single machine scheduling problems, Theoretical Computer Science 363 (2006) 257–265]. We provide the computation of an improved relative error of this heuristic, as well as a proof that this new bound is tight. We also present some computational experiments to test this heuristic on random instances. These experiments include an implementation of the fully-polynomial time approximation scheme given in Kacem and Ridha Mahjoub [I. Kacem, A. Ridha Mahjoub, Fully polynomial time approximation scheme for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers and Industrial Engineering 56 (2009) 1708–1712].