Scheduling independent tasks on multi-cores with GPU accelerators

International audienceMore and more computers use hybrid architectures combining multi-core processors and hardware accelerators like GPUs (Graphics Process-ing Units). We present in this paper a new method for scheduling efficiently parallel applications with m CPUs and k GPUs, where each task of the appli-cation can be processed either on a core (CPU) or on a GPU. The objective is to minimize the maximum completion time (makespan). The corresponding scheduling problem is NP-hard, we propose an efficient approximation algo-rithm which achieves an approximation ratio of 4 3 + 1 3k . We first detail and analyze the method, based on a dual approximation scheme, that uses dynamic programming to balance evenly the load between the heterogeneous resources. Then, we present a faster approximation algorithm for a special case of the previous problem, where all the tasks are accelerated when affected to GPU, with a performance guarantee of 3 2 for any number of GPUs. We run some simulations based on realistic benchmarks and compare the solutions obtained by a relaxed version of the generic method to the one provided by a classical scheduling algorithm (HEFT). Finally, we present an implementation of the 4/3-approximation and its relaxed version on a classical linear algebra kernel into the scheduler of the xKaapi runtime system

An EPTAS for Scheduling on Unrelated Machines of Few Different Types

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than $1.5$ unless P$=$NP. We consider the case that there are only a constant number $K$ of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for $K=1$. We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any $\varepsilon > 0$ an assignment with makespan of length at most $(1+\varepsilon)$ times the optimum can be found in polynomial time in the input length and the exponent is independent of $1/\varepsilon$. In particular we achieve a running time of $2^{\mathcal{O}(K\log(K) \frac{1}{\varepsilon}\log^4 \frac{1}{\varepsilon})}+\mathrm{poly}(|I|)$, where $|I|$ denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques

Spin Dynamics of Cavity Polaritons

We have studied polariton spin dynamics in a GaAs/AlGaAs microcavity by means of polarization- and time-resolved photoluminescence spectroscopy as a function of excitation density and normal mode splitting. The experiments reveal a novel behavior of the degree of polarization of the emission, namely the existence of a finite delay to reach its maximum value. We have also found that the stimulated emission of the lower polariton branch has a strong influence on spin dynamics: in an interval of $\sim$150 ps the polarization changes from +100% to negative values as high as -60%. This strong modulation of the polarization and its high speed may open new possibilities for spin-based devices.Comment: 4 pages, 3 eps figures, RevTeX, Physical Review B Rapid (submitted

Large and uniform optical emission shifts in quantum dots externally strained along their growth axis

We introduce a method which enables to directly compare the impact of elastic strain on the optical properties of distinct quantum dots (QDs). Specifically, the QDs are integrated in a cross-section of a semiconductor core wire which is surrounded by an amorphous straining shell. Detailed numerical simulations show that, thanks to the mechanical isotropy of the shell, the strain field in a core section is homogeneous. Furthermore, we use the core material as an in situ strain gauge, yielding reliable values for the emitter energy tuning slope. This calibration technique is applied to self-assembled InAs QDs submitted to incremental tensile strain along their growth axis. In contrast to recent studies conducted on similar QDs stressed perpendicularly to their growth axis, optical spectroscopy reveals 5-10 times larger tuning slopes, with a moderate dispersion. These results highlight the importance of the stress direction to optimise QD response to applied strain, with implications both in static and dynamic regimes. As such, they are in particular relevant for the development of wavelength-tunable single photon sources or hybrid QD opto-mechanical systems

Scheduling Independent Moldable Tasks on Multi-Cores with GPUs

The number of parallel systems using accelerators is growing up.The technology is now mature enough to allow sustainedpetaflop/s. However, reaching this performance scale requiresefficient scheduling algorithms to manage the heterogeneouscomputing resources.We present a new approach for scheduling independent tasks onmultiple CPUs and multiple GPUs. The tasks are assumed to beparallelizable on CPUs using the moldable model: the final numberof cores allotted to a task can be decided and set by thescheduler. More precisely, we design an algorithm aiming atminimizing the makespan---the maximum completion time of alltasks---for this scheduling problem. The proposed algorithmcombines a dual approximation scheme with a fast integer linearprogram (ILP). It determines both the partitioning of the tasks,ie whether a task should be mapped to CPUs or a GPU, and thenumber of CPUs allotted to a moldable task if mapped to the CPUs.A worst case analysis shows that the algorithm has anapproximation ratio of $\frac{3}{2} + \epsilon$. However, sincethe complexity of the ILP-based algorithm could benon-polynomial, we also present a proved polynomial-timealgorithm with an approximation ratio of $2+\epsilon$.We complement the theoretical analysis of our two novelalgorithms with an experimental study. In these experiments, wecompare our algorithms to a modified version of the classical\heft algorithm, adapted to handle moldable tasks. Theexperimental results show that our algorithm with the$\frac{3}{2} + \epsilon$ approximation ratio producessignificantly shorter schedules than the modified \heft for mostof the instances. In addition, the experiments provide evidencethat this ILP-based algorithm is also practically able to solvelarger problem instances in a reasonable amount of time

Theoretical analysis of quantum dynamics in 1D lattices: Wannier-Stark description

This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found.Comment: 8 pages, 6 figures, submitted to PR

Optical Study of GaAs quantum dots embedded into AlGaAs nanowires

We report on the photoluminescence characterization of GaAs quantum dots embedded into AlGaAs nano-wires. Time integrated and time resolved photoluminescence measurements from both an array and a single quantum dot/nano-wire are reported. The influence of the diameter sizes distribution is evidenced in the optical spectroscopy data together with the presence of various crystalline phases in the AlGaAs nanowires.Comment: 5 page, 5 figure

The Other In Henry Roth\u27s \u3ci\u3eCall It Sleep\u3c/i\u3e

This thesis project focuses on the notion of the Other in Henry Roth\u27s 1934 novel Call It Sleep. The novel follows David as his family moves to New York and struggles in poor areas. David\u27s inner world is rendered through a style which is reminiscent of a modernist stream of consciousness while retaining the realism of the 1930s proletarian novel. Call It Sleep is a rich text for the study of immigration and multi-culturalism and approaching the novel through the theme of the Other allows for multiple interpretations. The first chapter uses Jacques Lacan\u27s theories on Desire and analyzes David\u27s obsessive behavior toward objects representing purity. Lacanian Desire stems from lack and is transferred to objects that cannot bring satisfaction once attained. Lacan\u27s theories explain David\u27s quests and can be used to understand the \u27American Dream\u27 migrants followed as a spatial localization of this unattainable desire. The second chapter looks at Roth\u27s treatment of languages and identification of and with the Other. David is an Other for the two cultures he is in contact with and is either included or excluded by different languages. David\u27s identity as an Other fluctuates depending on which culture he is in contact with. Roth\u27s treatment of language and identities is still relevant as we struggle to find a balance between assimilation and multi-culturalism. The last chapter looks at Call It Sleep from a feminist point of view. In her essay \u27Women on the Market\u27, Luce Irigaray analyzes our society\u27s treatment of women as commodities and their exchanges. Irigaray\u27s theory allows for a unique perspective on the transition between a patriarchal society to a consumerist American society v where women are objectified. These different approaches allow for a comprehensive study of the Other in the text and inform on the different manifestations of the Other in our world, between the alienation of our desires, fragmentation of the self, the Otherness experienced in a multi-cultural society and the Othering of women. Analyzing Call It Sleep under these different lenses allow for a better understanding of the relation of the self and the Other for multi-cultural individuals