Speed Scaling for Maximum Lateness

We consider the power-aware problem of scheduling non-preemptively a set of jobs on a single speed-scalable processor so as to minimize the maximum lateness, under a given budget of energy. In the offline setting, our main contribution is a combinatorial polynomial time algorithm for the case in which the jobs have common release dates. In the presence of arbitrary release dates, we show that the problem becomes strongly \(\mathcal {N}\mathcal {P}\)-hard. Moreover, we show that there is no O(1)-competitive deterministic algorithm for the online setting in which the jobs arrive over time. Then, we turn our attention to an aggregated variant of the problem, where the objective is to find a schedule minimizing a linear combination of maximum lateness and energy. As we show, our results for the budget variant can be adapted to derive a similar polynomial time algorithm and an \(\mathcal {N}\mathcal {P}\)-hardness proof for the aggregated variant in the offline setting, with common and arbitrary release dates respectively. More interestingly, for the online case, we propose a 2-competitive algorithm.     

On truthfulness and approximation for scheduling selfish tasks

We consider the problem of designing truthful mechanisms for scheduling n tasks on a set of m parallel related machines in order to minimize the makespan. In what follows, we consider that each task is owned by a selfish agent. This is a variant of the KP-model introduced by Koutsoupias and Papadimitriou (Proc. of STACS 1999, pp. 404–413, 1999) (and of the CKN-model of Christodoulou et al. in Proc. of ICALP 2004, pp. 345–357, 2004) in which the agents cannot choose the machine on which their tasks will be executed. This is done by a centralized authority, the scheduler. However, the agents may manipulate the scheduler by providing false information regarding the length of their tasks. We introduce the notion of increasing algorithm and a simple reduction that transforms any increasing algorithm into a truthful one. Furthermore, we show that some of the classical scheduling algorithms are indeed increasing: the LPT algorithm, the PTAS of Graham (SIAM J. Appl. Math. 17(2):416–429, 1969) in the case of two machines, as well as a simple PTAS for the case of m machines, with m a fixed constant. Our results yield a randomized r(1+ε)-approximation algorithm where r is the ratio between the largest and the smallest speed of the related machines. Furthermore, by combining our approach with the classical result of Shmoys et al. (SIAM J. Comput. 24(6):1313–1331, 1995), we obtain a randomized 2r(1+ε)-competitive algorithm. It has to be noticed that these results are obtained without payments, unlike most of the existing works in the field of Mechanism Design. Finally, we show that if payments are allowed then our approach gives a (1+ε)-algorithm for the off-line case with related machines.     

Scheduling Independent Multiprocessor Tasks

We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm that finds a schedule of makespan within a factor of (1+\eps) of optimal in the non-preemptive model. We extend our results by obtaining a polynomial time approximation scheme for the parallel processors variant of the multiprocessor task model.     

Structure and thermoelectric properties of higher manganese silicides synthesized by pack cementation

Higher manganese silicides (HMS) are promising alternative materials for middle to high temperature thermoelectric applications as a low-cost, non-toxic and highly stable p-type leg. Many of the preparation methods that have been reported previously require long-time and energy consuming processes, as well as expensive equipment, and often do not result in a material of sufficient quality. In this study, the simple, cost-effective and eco-friendly technique of pack cementation is applied. HMS powders synthesized at different experimental conditions are studied and compared considering their structure, composition, short-term thermal stability in air and thermoelectric properties. X-ray diffraction analysis, X-ray photoelectron spectroscopy, scanning electron microscopy, thermogravimetry and thermoelectric measurements (in terms of Seebeck coefficient, electrical and thermal conductivity) were employed for the characterization of the material and evaluation of its performance. All samples were identified as HMS and only some negligible traces of MnSi were detected. They moderately oxidize when heated non-isothermally under air atmosphere up to 1473 K, while the presence of HMS remains dominant even at such high temperatures. Their thermoelectric properties were remarkable for an undoped material, with a maximum figure of merit (ZT) of 0.47 at 777 K. Pack cementation appeared to have a great potential as the synthesis route of high-efficiency HMS.     

Fair cost-sharing methods for the minimum spanning tree game

We study the problem of sharing in a fair manner the cost of a service provided to a set of players in the context of Cooperative Game Theory. We introduce a new fairness measure capturing the dissatisfaction (or happiness) of each player and we propose two cost sharing methods minimizing the maximum or average dissatisfaction of the clients for the classical minimum spanning tree game.     

Scheduling Independent Multiprocessor Tasks

Abstract. We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm that finds a schedule of makespan within a factor of (1+\eps) of optimal in the non-preemptive model. We extend our results by obtaining a polynomial time approximation scheme for the parallel processors variant of the multiprocessor task model.     

Scheduling trees with large communication delays on two identical processors

We consider the problem of scheduling trees on two identical processors in order to minimize the makespan. We assume that tasks have unit execution times, and arcs are associated with large identical integer communication delays. We prove that the problem is NP-hard in the strong sense even when restricted to the class of binary trees, and we provide a polynomial-time algorithm for complete binary trees.This work has been partially supported by the French-Greek bilateral exchange program PLATON and the GDR-PRS Ordonnancement pour le parallélisme program of the French government.     

Calibrations scheduling with arbitrary lengths and activation length

Bender et al. (SPAA 2013) proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be calibrated on a regular basis. Since calibrations have a non-negligible cost, it is important to study policies minimizing the total calibration cost while performing all the necessary tests. We focus on the single-machine setting, and we study the complexity status of different variants of the problem. First, we extend the model by considering that the jobs have arbitrary processing times, and we propose an optimal polynomial-time algorithm when the preemption of jobs is allowed. Then, we study the case where there are many types of calibrations with their corresponding lengths and costs. We prove that the problem becomes NP-hard for arbitrary processing times even when the preemption of the jobs is allowed. Finally, we focus on the case of unit processing time jobs, and we show that a more general problem, where the recalibration of the machine is not instantaneous, can be solved in polynomial time via dynamic programming.

     

Does High Hydrostatic Pressure Affect Fruit Esters?

The effect of high hydrostatic pressure on ester formation and hydrolysis was studied. Six esters and the corresponding carboxylic acids and alcohols were subjected to high-pressure treatments of 400 and 800 MPa under three different pH conditions (namely, buffer solutions of pH 4, 6 and 8). The selected compounds were dissolved into buffer solutions, subjected to the pressure treatment and then extracted using dichloromethane. The analysis and quantification were carried out by gas chromatography with flame ionization as detector. High pressure appeared to have no effect on ester formation or hydrolysis under the investigated conditions. In all cases, a small decrease at the levels of carboxylic acids and esters was observed without any evidence of further reaction. This decrease, referred to as decomposition, depended on pressure and pH conditions. Ester decomposition was minimised when a high-pressure treatment of 400 MPa in basic conditions (pH 8) was applied. Carboxylic acid decomposition was minimal in basic conditions and it was independent of the pressure applied.