509 research outputs found
Scheduling multiple divisible loads on a linear processor network
Min, Veeravalli, and Barlas have recently proposed strategies to minimize the
overall execution time of one or several divisible loads on a heterogeneous
linear network, using one or more installments. We show on a very simple
example that their approach does not always produce a solution and that, when
it does, the solution is often suboptimal. We also show how to find an optimal
schedule for any instance, once the number of installments per load is given.
Then, we formally state that any optimal schedule has an infinite number of
installments under a linear cost model as the one assumed in the original
papers. Therefore, such a cost model cannot be used to design practical
multi-installment strategies. Finally, through extensive simulations we
confirmed that the best solution is always produced by the linear programming
approach, while solutions of the original papers can be far away from the
optimal
Current fluctuations in systems with diffusive dynamics, in and out of equilibrium
For diffusive systems that can be described by fluctuating hydrodynamics and
by the Macroscopic Fluctuation Theory of Bertini et al., the total current
fluctuations display universal features when the system is closed and in
equilibrium. When the system is taken out of equilibrium by a boundary-drive,
current fluctuations, at least for a particular family of diffusive systems,
display the same universal features as in equilibrium. To achieve this result,
we exploit a mapping between the fluctuations in a boundary-driven
nonequilibrium system and those in its equilibrium counterpart. Finally, we
prove, for two well-studied processes, namely the Simple Symmetric Exclusion
Process and the Kipnis-Marchioro-Presutti model for heat conduction, that the
distribution of the current out of equilibrium can be deduced from the
distribution in equilibrium. Thus, for these two microscopic models, the
mapping between the out-of-equilibrium setting and the equilibrium one is
exact
Equilibrium-like fluctuations in some boundary-driven open diffusive systems
There exist some boundary-driven open systems with diffusive dynamics whose
particle current fluctuations exhibit universal features that belong to the
Edwards-Wilkinson universality class. We achieve this result by establishing a
mapping, for the system's fluctuations, to an equivalent open --yet
equilibrium-- diffusive system. We discuss the possibility of observing dynamic
phase transitions using the particle current as a control parameter
Checkpointing algorithms and fault prediction
This paper deals with the impact of fault prediction techniques on
checkpointing strategies. We extend the classical first-order analysis of Young
and Daly in the presence of a fault prediction system, characterized by its
recall and its precision. In this framework, we provide an optimal algorithm to
decide when to take predictions into account, and we derive the optimal value
of the checkpointing period. These results allow to analytically assess the key
parameters that impact the performance of fault predictors at very large scale.Comment: Supported in part by ANR Rescue. Published in Journal of Parallel and
Distributed Computing. arXiv admin note: text overlap with arXiv:1207.693
Building a path-integral calculus: a covariant discretization approach
Path integrals are a central tool when it comes to describing quantum or
thermal fluctuations of particles or fields. Their success dates back to
Feynman who showed how to use them within the framework of quantum mechanics.
Since then, path integrals have pervaded all areas of physics where fluctuation
effects, quantum and/or thermal, are of paramount importance. Their appeal is
based on the fact that one converts a problem formulated in terms of operators
into one of sampling classical paths with a given weight. Path integrals are
the mirror image of our conventional Riemann integrals, with functions
replacing the real numbers one usually sums over. However, unlike conventional
integrals, path integration suffers a serious drawback: in general, one cannot
make non-linear changes of variables without committing an error of some sort.
Thus, no path-integral based calculus is possible. Here we identify which are
the deep mathematical reasons causing this important caveat, and we come up
with cures for systems described by one degree of freedom. Our main result is a
construction of path integration free of this longstanding problem, through a
direct time-discretization procedure.Comment: 22 pages, 2 figures, 1 table. Typos correcte
Finite size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality
On the example of a mean-field Fredrickson-Andersen kinetically constrained
model, we focus on the known property that equilibrium dynamics take place at a
first-order dynamical phase transition point in the space of time-realizations.
We investigate the finite-size properties of this first order transition. By
discussing and exploiting a mapping of the classical dynamical transition -an
argued glassiness signature- to a first-order quantum transition, we show that
the quantum analogy can be exploited to extract finite-size properties, which
in many respects are similar to those in genuine mean-field quantum systems
with a first-order transition. We fully characterize the finite-size properties
of the order parameter across the first order transition
Activity statistics in a colloidal glass former: experimental evidence for a dynamical transition
In a dense colloidal suspension at a volume fraction slightly lower than that
of its glass transition, we follow the trajectories of an assembly of tracers
over a large time window. We define a local activity, which quantifies the
local tendency of the system to rearrange. We determine the statistics of the
time and space integrated activity, and we argue that it develops a low
activity tail that comes on a par with the onset of glassy behavior and
heterogeneous dynamics. These rare events may be interpreted as the reflection
of an underlying dynamic phase transition.Comment: 20 pages, 16 figure
Impact of fault prediction on checkpointing strategies
This paper deals with the impact of fault prediction techniques on
checkpointing strategies. We extend the classical analysis of Young and Daly in
the presence of a fault prediction system, which is characterized by its recall
and its precision, and which provides either exact or window-based time
predictions. We succeed in deriving the optimal value of the checkpointing
period (thereby minimizing the waste of resource usage due to checkpoint
overhead) in all scenarios. These results allow to analytically assess the key
parameters that impact the performance of fault predictors at very large scale.
In addition, the results of this analytical evaluation are nicely corroborated
by a comprehensive set of simulations, thereby demonstrating the validity of
the model and the accuracy of the results.Comment: 20 page
Scheduling malleable task trees
Solving sparse linear systems can lead to processing tree workflows on a platform of processors. In this study, we use the model of malleable tasks motivated in [Prasanna96,Beaumont07] in order to study tree workflow schedules under two contradictory objectives: makespan minimization and memory minization. First, we give a simpler proof of the result of [Prasanna96] which allows to compute a makespan-optimal schedule for tree workflows. Then, we study a more realistic speed-up function and show that the previous schedules are not optimal in this context. Finally, we give complexity results concerning the objective of minimizing both makespan and memory
A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis
International audiencePresenting a complementary perspective to standard books on algorithms, A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis provides a roadmap for readers to determine the difficulty of an algorithmic problem by finding an optimal solution or proving complexity results. It gives a practical treatment of algorithmic complexity and guides readers in solving algorithmic problems. Divided into three parts, the book offers a comprehensive set of problems with solutions as well as in-depth case studies that demonstrate how to assess the complexity of a new problem. Part I helps readers understand the main design principles and design efficient algorithms. Part II covers polynomial reductions from NP-complete problems and approaches that go beyond NP-completeness. Part III supplies readers with tools and techniques to evaluate problem complexity, including how to determine which instances are polynomial and which are NP-hard. Drawing on the authors' classroom-tested material, this text takes readers step by step through the concepts and methods for analyzing algorithmic complexity. Through many problems and detailed examples, readers can investigate polynomial-time algorithms and NP-completeness and beyond
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