Some complexity and approximation results for coupled-tasks scheduling problem according to topology

We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain,. . .). In such a context, we design some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters

Reclaiming the energy of a schedule: models and algorithms

We consider a task graph to be executed on a set of processors. We assume that the mapping is given, say by an ordered list of tasks to execute on each processor, and we aim at optimizing the energy consumption while enforcing a prescribed bound on the execution time. While it is not possible to change the allocation of a task, it is possible to change its speed. Rather than using a local approach such as backfilling, we consider the problem as a whole and study the impact of several speed variation models on its complexity. For continuous speeds, we give a closed-form formula for trees and series-parallel graphs, and we cast the problem into a geometric programming problem for general directed acyclic graphs. We show that the classical dynamic voltage and frequency scaling (DVFS) model with discrete modes leads to a NP-complete problem, even if the modes are regularly distributed (an important particular case in practice, which we analyze as the incremental model). On the contrary, the VDD-hopping model leads to a polynomial solution. Finally, we provide an approximation algorithm for the incremental model, which we extend for the general DVFS model.Comment: A two-page extended abstract of this work appeared as a short presentation in SPAA'2011, while the long version has been accepted for publication in "Concurrency and Computation: Practice and Experience

Many-Task Computing and Blue Waters

This report discusses many-task computing (MTC) generically and in the context of the proposed Blue Waters systems, which is planned to be the largest NSF-funded supercomputer when it begins production use in 2012. The aim of this report is to inform the BW project about MTC, including understanding aspects of MTC applications that can be used to characterize the domain and understanding the implications of these aspects to middleware and policies. Many MTC applications do not neatly fit the stereotypes of high-performance computing (HPC) or high-throughput computing (HTC) applications. Like HTC applications, by definition MTC applications are structured as graphs of discrete tasks, with explicit input and output dependencies forming the graph edges. However, MTC applications have significant features that distinguish them from typical HTC applications. In particular, different engineering constraints for hardware and software must be met in order to support these applications. HTC applications have traditionally run on platforms such as grids and clusters, through either workflow systems or parallel programming systems. MTC applications, in contrast, will often demand a short time to solution, may be communication intensive or data intensive, and may comprise very short tasks. Therefore, hardware and software for MTC must be engineered to support the additional communication and I/O and must minimize task dispatch overheads. The hardware of large-scale HPC systems, with its high degree of parallelism and support for intensive communication, is well suited for MTC applications. However, HPC systems often lack a dynamic resource-provisioning feature, are not ideal for task communication via the file system, and have an I/O system that is not optimized for MTC-style applications. Hence, additional software support is likely to be required to gain full benefit from the HPC hardware

Scheduling stretched coupled-tasks with compatibilities constraints : model, complexity and approximation results for some class of graphs

We tackle the makespan minimization coupled-tasks problem in presence of compatibility constraints. In particular, we focus on stretched coupled-tasks, {\it i.e.}coupled-tasks having the same sub-tasks execution time and idle time duration. We study severals problems in frame works of classic complexity and approximation for which the compatibility graph $G_c$ is bipartite (star, chain, $\ldots$) In such context, we design some efficient polynomial-time approximation algorithms according to difference parameters of the scheduling problem. When $G_c$ is a $k$-stage bipartite graph, we propose, among other, a $\frac{7}{6}$-approximation algorithm when $k=1$, and a $\frac{13}{9}$-approximation algorithm when $k=2$.\

A Taxonomy for Management and Optimization of Multiple Resources in Edge Computing

Edge computing is promoted to meet increasing performance needs of data-driven services using computational and storage resources close to the end devices, at the edge of the current network. To achieve higher performance in this new paradigm one has to consider how to combine the efficiency of resource usage at all three layers of architecture: end devices, edge devices, and the cloud. While cloud capacity is elastically extendable, end devices and edge devices are to various degrees resource-constrained. Hence, an efficient resource management is essential to make edge computing a reality. In this work, we first present terminology and architectures to characterize current works within the field of edge computing. Then, we review a wide range of recent articles and categorize relevant aspects in terms of 4 perspectives: resource type, resource management objective, resource location, and resource use. This taxonomy and the ensuing analysis is used to identify some gaps in the existing research. Among several research gaps, we found that research is less prevalent on data, storage, and energy as a resource, and less extensive towards the estimation, discovery and sharing objectives. As for resource types, the most well-studied resources are computation and communication resources. Our analysis shows that resource management at the edge requires a deeper understanding of how methods applied at different levels and geared towards different resource types interact. Specifically, the impact of mobility and collaboration schemes requiring incentives are expected to be different in edge architectures compared to the classic cloud solutions. Finally, we find that fewer works are dedicated to the study of non-functional properties or to quantifying the footprint of resource management techniques, including edge-specific means of migrating data and services.Comment: Accepted in the Special Issue Mobile Edge Computing of the Wireless Communications and Mobile Computing journa

Cross-layer design of multi-hop wireless networks

MULTI -hop wireless networks are usually defined as a collection of nodes equipped with radio transmitters, which not only have the capability to communicate each other in a multi-hop fashion, but also to route each others’ data packets. The distributed nature of such networks makes them suitable for a variety of applications where there are no assumed reliable central entities, or controllers, and may significantly improve the scalability issues of conventional single-hop wireless networks. This Ph.D. dissertation mainly investigates two aspects of the research issues related to the efficient multi-hop wireless networks design, namely: (a) network protocols and (b) network management, both in cross-layer design paradigms to ensure the notion of service quality, such as quality of service (QoS) in wireless mesh networks (WMNs) for backhaul applications and quality of information (QoI) in wireless sensor networks (WSNs) for sensing tasks. Throughout the presentation of this Ph.D. dissertation, different network settings are used as illustrative examples, however the proposed algorithms, methodologies, protocols, and models are not restricted in the considered networks, but rather have wide applicability. First, this dissertation proposes a cross-layer design framework integrating a distributed proportional-fair scheduler and a QoS routing algorithm, while using WMNs as an illustrative example. The proposed approach has significant performance gain compared with other network protocols. Second, this dissertation proposes a generic admission control methodology for any packet network, wired and wireless, by modeling the network as a black box, and using a generic mathematical 0. Abstract 3 function and Taylor expansion to capture the admission impact. Third, this dissertation further enhances the previous designs by proposing a negotiation process, to bridge the applications’ service quality demands and the resource management, while using WSNs as an illustrative example. This approach allows the negotiation among different service classes and WSN resource allocations to reach the optimal operational status. Finally, the guarantees of the service quality are extended to the environment of multiple, disconnected, mobile subnetworks, where the question of how to maintain communications using dynamically controlled, unmanned data ferries is investigated