Non-Preemptive Flow-Time Minimization via Rejections

We consider the online problem of minimizing weighted flow-time on unrelated machines. Although much is known about this problem in the resource-augmentation setting, these results assume that jobs can be preempted. We give the first constant-competitive algorithm for the non-preemptive setting in the rejection model. In this rejection model, we are allowed to reject an epsilon-fraction of the total weight of jobs, and compare the resulting flow-time to that of the offline optimum which is required to schedule all jobs. This is arguably the weakest assumption in which such a result is known for weighted flow-time on unrelated machines. While our algorithms are simple, we need a delicate argument to bound the flow-time. Indeed, we use the dual-fitting framework, with considerable more machinery to certify that the cost of our algorithm is within a constant of the optimum while only a small fraction of the jobs are rejected

Notes on Max Flow Time Minimization with Controllable Processing Times

In a scheduling problem with controllable processing times the job processing time can be compressed through incurring an additional cost. We consider the identical parallel machines max flow time minimization problem with controllable processing times. We address the preemptive and non-preemptive version of the problem. For the preemptive case, a linear programming formulation is presented which solves the problem optimally in polynomial time. For the non-preemptive problem it is shown that the First In First Out (FIFO) heuristic has a tight worst-case performance of 3−2/m, when jobs processing times and costs are set as in some optimal preemptive schedul

Minimizing Flow-Time on Unrelated Machines

We consider some flow-time minimization problems in the unrelated machines setting. In this setting, there is a set of $m$ machines and a set of $n$ jobs, and each job $j$ has a machine dependent processing time of $p_{ij}$ on machine $i$. The flow-time of a job is the total time the job spends in the system (completion time minus its arrival time), and is one of the most natural quality of service measure. We show the following two results: an $O(\min(\log^2 n,\log n \log P))$ approximation algorithm for minimizing the total-flow time, and an $O(\log n)$ approximation for minimizing the maximum flow-time. Here $P$ is the ratio of maximum to minimum job size. These are the first known poly-logarithmic guarantees for both the problems.Comment: The new version fixes some typos in the previous version. The paper is accepted for publication in STOC 201

Efficient heuristic algorithms for the blocking flow shop scheduling problem with total flow time minimization

This paper proposes two constructive heuristics, i.e. HPF1 and HPF2, for the blocking flow shop problem in order to minimize the total flow time. They differ mainly in the criterion used to select the first job in the sequence since, as it is shown, its contribution to the total flow time is not negligible. Both procedures were combined with the insertion phase of NEH to improve the sequence. However, as the insertion procedure does not always improve the solution, in the resulting heuristics, named NHPF1 and NHPF2, the sequence was evaluated before and after the insertion to keep the best of both solutions. The structure of these heuristics was used in Greedy Randomized Adaptive Search Procedures (GRASP) with variable neighborhood search in the improvement phase to generate greedy randomized solutions. The performance of the constructive heuristics and of the proposed GRASPs was evaluated against other heuristics from the literature. Our computational analysis showed that the presented heuristics are very competitive and able to improve 68 out of 120 best known solutions of Taillard’s instances for the blocking flow shop scheduling problem with the total flow time criterionPeer ReviewedPostprint (author’s final draft

Heuristics for the distributed blocking Ffow shop scheduling problem

Postprint (published version

Flow-time minimization for timely data stream processing in UAV-aided mobile edge computing

Unmanned Aerial Vehicle (UAV) has gained increasing attentions by both academic and industrial communities, due to its flexible deployment and efficient line-of-sight communication. Recently, UAVs equipped with base stations have been envisioned as a key technology to provide 5G network services for mobile users. In this paper, we provide timely services on the data streams of mobile users in a UAV-aided Mobile Edge Computing (MEC) network, in which each UAV is equipped with a 5G small-cell base station for communication and data processing. Specifically, we first formulate a flow-time minimization problem by jointly caching services and offloading tasks of mobile users to the UAV-aided MEC with the aim to minimize the flow-time, where the flow-time of a user request is referred to the time duration from the request issuing time point to its completion point, subject to resource and energy capacity on each UAV. We then propose a spatial-temporal learning optimization framework. We also devise an online algorithm with a competitive ratio for the problem based upon the framework, by leveraging the round-robin scheduling and dual fitting techniques. Finally, we evaluate the performance of the proposed algorithms through experimental simulation. The simulation results demonstrated that the proposed algorithms outperform their comparison counterparts, by reducing the flow-time no less than 19% on average

From Preemptive to Non-preemptive Scheduling Using Rejections

International audienceWe study the classical problem of scheduling a set of independent jobs with release dates on a single machine. There exists a huge literature on the preemptive version of the problem, where the jobs can be interrupted at any moment. However, we focus here on the non-preemptive case, which is harder, but more relevant in practice. For instance, the jobs submitted to actual high performance platforms cannot be interrupted or migrated once they start their execution (due to prohibitive management overhead). We target on the minimization of the total stretch objective, defined as the ratio of the total time a job stays in the system (waiting time plus execution time), normalized by its processing time. Stretch captures the quality of service of a job and the minimum total stretch reflects the fairness between the jobs. So far, there have been only few studies about this problem, especially for the non-preemptive case. Our approach is based to the usage of the classical and efficient for the preemptive case shortest remaining processing time (SRPT) policy as a lower bound. We investigate the (offline) transformation of the SRPT schedule to a non-preemptive schedule subject to a recently introduced resource augmentation model, namely the rejection model according to which we are allowed to reject a small fraction of jobs. Specifically, we propose a 2 ǫ-approximation algorithm for the total stretch minimization problem if we allow to reject an ǫ-fraction of the jobs, for any ǫ > 0. This result shows that the rejection model is more powerful than the other resource augmentations models studied in the literature, like speed augmentation or machine augmentation, for which non-polynomial or non-scalable results are known. As a byproduct, we present a O(1)-approximation algorithm for the total flow-time minimization problem which also rejects at most an \epsilon-fraction of jobs

Development and characterization of treated kaolin filled polypropylene/kaolin nanocomposites

This research work focused on producing modified kaolin filler in polypropylene/kaolin (PP/K) nanocomposite by melt compounding process in order to improve its mechanical and thermal properties for industrial applications. The surface treatments of micron sized Malaysian kaolin were conducted to produce nano sized kaolin by acidification of kaolin fillers with sulphuric acid and planetary milling using urea (mechanochemical milling). Testing on both surface treated kaolin were carried out with the aid of Field Scanning Electron Microscopy (FESEM), Fourier Transform Infrared (FTIR), Brunauer–Emmett–Teller (BET), X-ray Diffraction (XRD) and Particle Size Analyser and results of both treated kaolin were compared. However, the surface treated kaolin using acidification was unsuccessful as shown by XRD, FTIR and BET results. A successful delamination of micron sized into nano sized kaolin was achieved by mechanochemical milling. The additional bands at 3624, 3445 and 3388 cm-1 and illite phase at lower 2θ by FTIR and XRD studies respectively, indicated delamination of kaolin. Surface area increased by 400% from BET results. The PP/K nanocomposite was produced by incorporating low weight (1-7%) percentages of organically modified nanokaolin into PP by melt compounding with polypropylene grafted maleic anhydride (PP-g-MA) as coupling agent. The FTIR and XRD analyses on chemical structure showed successful synthesis of PP/K nanocomposites by the vanishing of characteristic of OH bands and peaks of kaolin respectively. The tensile and impact strength, tan δ, loss modulus and melt flow index of PP/K nanocomposite decreases by 17, 27, 36, 32 and 78% respectively. Conversely, the results show that incorporation of nanokaolin clay into PP causes increase in thermal degradation (200%), crystalinity (17%), nucleation effect (17%), storage modulus (10%), surface roughness (87%), and optical (262%). Whereas, TEM of PP/K nanocomposite exhibit nanokaolin dispersion with nanoscale sizes. Therefore, the PP/K nanocomposites formulated shall be a potential candidate for manufacturing novel new materials of attraction in many sectors