Asymptotically Optimal Approximation Algorithms for Coflow Scheduling

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a {\em coflow}, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal. In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an $O(\log n/\log \log n)$-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here $n$ is the number of network edges). We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least 22% on average over competing heuristics.Comment: Fixed minor typo

Scheduling Jobs in Flowshops with the Introduction of Additional Machines in the Future

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/expert-systems-with-applications/.The problem of scheduling jobs to minimize total weighted tardiness in flowshops,\ud with the possibility of evolving into hybrid flowshops in the future, is investigated in\ud this paper. As this research is guided by a real problem in industry, the flowshop\ud considered has considerable flexibility, which stimulated the development of an\ud innovative methodology for this research. Each stage of the flowshop currently has\ud one or several identical machines. However, the manufacturing company is planning\ud to introduce additional machines with different capabilities in different stages in the\ud near future. Thus, the algorithm proposed and developed for the problem is not only\ud capable of solving the current flow line configuration but also the potential new\ud configurations that may result in the future. A meta-heuristic search algorithm based\ud on Tabu search is developed to solve this NP-hard, industry-guided problem. Six\ud different initial solution finding mechanisms are proposed. A carefully planned\ud nested split-plot design is performed to test the significance of different factors and\ud their impact on the performance of the different algorithms. To the best of our\ud knowledge, this research is the first of its kind that attempts to solve an industry-guided\ud problem with the concern for future developments

A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs

Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms

Energy-Efficient Multiprocessor Scheduling for Flow Time and Makespan

We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power $s^{\alpha}$ when running at speed $s$, for $\alpha>1$. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with time-varying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelism clairvoyant (IP-clairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an $O(1)$-competitive algorithm, which significantly improves upon the best known non-clairvoyant algorithm and is the first constant competitive result on multiprocessor speed scaling for parallel jobs. In the case of makespan plus energy, which is considered for the first time in the literature, we present an $O(\ln^{1-1/\alpha}P)$-competitive algorithm, where $P$ is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we also study non-clairvoyant scheduling for total flow time plus energy, and present an algorithm that achieves $O(\ln P)$-competitive for jobs with arbitrary release time and $O(\ln^{1/\alpha}P)$-competitive for jobs with identical release time. Finally, we prove an $\Omega(\ln^{1/\alpha}P)$ lower bound on the competitive ratio of any non-clairvoyant algorithm, matching the upper bound of our algorithm for jobs with identical release time