Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives such as makespan and weighted completion time. For many problems, we develop nearly-linear time approximation algorithms with approximation ratios matching the current best ones achieved in polynomial time. Our main technique is linear programming relaxation. For the unrelated machine setting, we formulate mixed packing and covering LP relaxations of nearly-linear size, and solve them approximately using the nearly-linear time solver of Young. For the makespan objective, we develop a rounding algorithm with (2+?)-approximation ratio. For the weighted completion time objective, we prove the LP is as strong as the rectangle LP used by Im and Li, leading to a nearly-linear time (1.45 + ?)-approximation for the problem. For problems in the identical machine with precedence constraints setting, the precedence constraints can not be formulated as packing or covering constraints. To achieve the nearly-linear running time, we define a polytope for the constraints, and leverage the multiplicative weight update (MWU) method with an oracle which always returns solutions in the polytope

Nearly-Linear Time Approximate Scheduling Algorithms

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting. The objectives we study include makespan, weighted completion time, and $L_q$ norm of machine loads. We develop nearly-linear time approximation algorithms for the studied problems with $O(1)$-approximation ratios, many of which match the correspondent best known ratios achievable in polynomial time. Our main technique is linear programming relaxation. For problems in the unrelated machine setting, we formulate mixed packing and covering LP relaxations of nearly-linear size, and solve them approximately using the nearly-linear time solver of Young. We show the LP solutions can be rounded within $O(1)$-factor loss. For problems in the identical machine with precedence constraints setting, the precedence constraints can not be formulated as packing or covering constraints. To achieve the claimed running time, we define a polytope for the constraints, and leverage the multiplicative weight update (MWU) method with an oracle which always returns solutions in the polytope. Along the way of designing the oracle, we encounter the single-commodity maximum flow problem over a directed acyclic graph $G = (V, E)$, where sources and sinks have limited supplies and demands, but edges have infinite capacities. We develop a $\frac{1}{1+\epsilon}$-approximation for the problem in time $O\left(\frac{|E|}{\epsilon}\log |V|\right)$, which may be of independent interest

Algorithms for Scheduling Problems

This edited book presents new results in the area of algorithm development for different types of scheduling problems. In eleven chapters, algorithms for single machine problems, flow-shop and job-shop scheduling problems (including their hybrid (flexible) variants), the resource-constrained project scheduling problem, scheduling problems in complex manufacturing systems and supply chains, and workflow scheduling problems are given. The chapters address such subjects as insertion heuristics for energy-efficient scheduling, the re-scheduling of train traffic in real time, control algorithms for short-term scheduling in manufacturing systems, bi-objective optimization of tortilla production, scheduling problems with uncertain (interval) processing times, workflow scheduling for digital signal processor (DSP) clusters, and many more

Scheduling for Large Scale Distributed Computing Systems: Approaches and Performance Evaluation Issues

Although our everyday life and society now depends heavily oncommunication infrastructures and computation infrastructures,scientists and engineers have always been among the main consumers ofcomputing power. This document provides a coherent overview of theresearch I have conducted in the last 15 years and which targets themanagement and performance evaluation of large scale distributedcomputing infrastructures such as clusters, grids, desktop grids,volunteer computing platforms, ... when used for scientific computing.In the first part of this document, I present how I have addressedscheduling problems arising on distributed platforms (like computinggrids) with a particular emphasis on heterogeneity and multi-userissues, hence in connection with game theory. Most of these problemsare relaxed from a classical combinatorial optimization formulationinto a continuous form, which allows to easily account for keyplatform characteristics such as heterogeneity or complex topologywhile providing efficient practical and distributed solutions.The second part presents my main contributions to the SimGrid project,which is a simulation toolkit for building simulators of distributedapplications (originally designed for scheduling algorithm evaluationpurposes). It comprises a unified presentation of how the questions ofvalidation and scalability have been addressed in SimGrid as well asthoughts on specific challenges related to methodological aspects andto the application of SimGrid to the HPC context

Overlapping of Communication and Computation and Early Binding: Fundamental Mechanisms for Improving Parallel Performance on Clusters of Workstations

This study considers software techniques for improving performance on clusters of workstations and approaches for designing message-passing middleware that facilitate scalable, parallel processing. Early binding and overlapping of communication and computation are identified as fundamental approaches for improving parallel performance and scalability on clusters. Currently, cluster computers using the Message-Passing Interface for interprocess communication are the predominant choice for building high-performance computing facilities, which makes the findings of this work relevant to a wide audience from the areas of high-performance computing and parallel processing. The performance-enhancing techniques studied in this work are presently underutilized in practice because of the lack of adequate support by existing message-passing libraries and are also rarely considered by parallel algorithm designers. Furthermore, commonly accepted methods for performance analysis and evaluation of parallel systems omit these techniques and focus primarily on more obvious communication characteristics such as latency and bandwidth. This study provides a theoretical framework for describing early binding and overlapping of communication and computation in models for parallel programming. This framework defines four new performance metrics that facilitate new approaches for performance analysis of parallel systems and algorithms. This dissertation provides experimental data that validate the correctness and accuracy of the performance analysis based on the new framework. The theoretical results of this performance analysis can be used by designers of parallel system and application software for assessing the quality of their implementations and for predicting the effective performance benefits of early binding and overlapping. This work presents MPI/Pro, a new MPI implementation that is specifically optimized for clusters of workstations interconnected with high-speed networks. This MPI implementation emphasizes features such as persistent communication, asynchronous processing, low processor overhead, and independent message progress. These features are identified as critical for delivering maximum performance to applications. The experimental section of this dissertation demonstrates the capability of MPI/Pro to facilitate software techniques that result in significant application performance improvements. Specific demonstrations with Virtual Interface Architecture and TCP/IP over Ethernet are offered

Bridging a Gap Between Research and Production: Contributions to Scheduling and Simulation

Large scale distributed computing infrastructures (e.g., data centers, grids, or clouds) are used by scientists from various domains to produce outstanding research results, such as the discovery of the Higgs Boson in High Energy Physics. These infrastructures are also studied by Computer Scientists to produce their own set of scientific results. Ideally, a virtuous circle should exist between Domain and Computer Scientists: the former raising challenges that could be addressed by the latter. Unfortunately, in many occasions, a gap exists that prevents such an ideal and fostering collaboration. This habilitation covers research works conducted in the fields of scheduling and simulation that contribute to the filling of this gap. It discusses the necessary conditions to achieve this goal and details concrete initiatives in this endeavor

Efficient Learning Machines

Computer scienc