A best-compromise bicriteria scheduling algorithm for malleable tasks

We consider in this paper the problem of scheduling a set of inde- pendent parallel tasks (jobs) with respect to two criteria, namely, the makespan (time of the last finishing job) and the minsum (average completion time). There exist several algorithms with a good performance guaranty for one of these criteria. We are interested here in studying the optimization of both criteria simultaneously. The numerical values are given for the moldable task model, where the execution time of a task depends on the number of processors alloted to it. The main result of this paper is to derive explicitly a family of algorithms guaranteed for both the minsum and the makespan. The performance guaranty of these algorithms is better than the best algorithms known so far. The Guaranty curve of the family is the set of all points (x; y) such that there is an algorithm with guarantees x on makespan and y on the min-sum. When the ratio on the minsum increases, the curve tends to the best ratio known for the makespan for moldable tasks (3/2). One extremal point of the curves is a (3;6)-approximation algorithm. Finally a randomized version is given, which improves this results to (3;4.08)

Online Bicriteria Load Balancing using Object Reallocation

Cataloged from PDF version of article.We study the bicriteria load balancing problem on two independent parameters under the allowance of object reallocation. The scenario is a system of M distributed file servers located in a cluster, and we propose three online approximate algorithms for balancing their loads and required storage spaces during document placement. The first algorithm is for heterogeneous servers. Each server has its individual trade-off of load and storage space under the same rule of selection. The other two algorithms are for homogeneous servers. The second algorithm combines the idea of the first one and the best existing solution for homogeneous servers. Using document reallocation, we obtain a smooth trade-off curve of the upper bounds of load and storage space. The last one bounds the load and storage space of each server by less than three times of their trivial lower bounds, respectively; and more importantly, for each server, the value of at least one parameter is far from its worst case. The time complexities of these three algorithms are O(log M) plus the cost of document reallocation

Machine speed scaling by adapting methods for convex optimization with submodular constraints

In this paper, we propose a new methodology for the speed-scaling problem based on its link to scheduling with controllable processing times and submodular optimization. It results in faster algorithms for traditional speed-scaling models, characterized by a common speed/energy function. Additionally, it efficiently handles the most general models with job-dependent speed/energy functions with single and multiple machines. To the best of our knowledge, this has not been addressed prior to this study. In particular, the general version of the single-machine case is solvable by the new technique in O(n2) time

Scheduling Parallel Jobs to Minimize Makespan

We consider the NP-hard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a pre-specified, job-dependent number of machines when being processed. Our main result is the following. The makespan of a (non-preemptive) schedule constructed by any listscheduling algorithm is within a factor of 2 of the optimal preemptive makespan. This gives the best known approximation algorithms for both the preemptive and the non-preemptive variant of the problem, improving upon previously known performance guarantees of 3. We also show that no listscheduling algorithm can achieve a better performance guarantee than 2 for the non-preemptive problem, no matter which priority list is chosen. Since listscheduling also works in the online setting in which jobs arrive over time and the length of a job becomes only known when it completes, the main result yields a deterministic online algorithm with competitive ratio 2 as well. In addition, we consider a different online model in which jobs arrive one by one and need to be scheduled before the next job becomes known. In this context, no listscheduling algorithm has a constant competitive ratio. We present the first online algorithm for scheduling parallel jobs with a constant competitive ratio. We also prove a new information-theoretic lower bound of 2:25 for the competitive ratio of any deterministic online algorithm for this model

Tradeoff exploration between reliability, power consumption, and execution time for embedded systems

International audienceFor autonomous critical real-time embedded systems (e.g., satellite), guaranteeing a very high level of reliability is as important as keeping the power consumption as low as possible. We propose an off-line scheduling heuristic which, from a given software application graph and a given multiprocessor architecture (homogeneous and fully connected), produces a static multiprocessor schedule that optimizes three criteria: its length (crucial for real-time systems), its reliability (crucial for dependable systems), and its power consumption (crucial for autonomous systems). Our tricriteria scheduling heuristic, called TSH, uses the active replication of the operations and the data-dependencies to increase the reliability and uses dynamic voltage and frequency scaling to lower the power consumption. We demonstrate the soundness of TSH. We also provide extensive simulation results to show how TSH behaves in practice: first, we run TSH on a single instance to provide the whole Pareto front in 3D; second, we compare TSH versus the ECS heuristic (Energy-Conscious Scheduling) from the literature; and third, we compare TSH versus an optimal Mixed Linear Integer Program

Scheduling Malleable Tasks with Precedence Constraints

In this paper we propose an approximation algorithm for scheduling malleable tasks with precedence constraints. Based on an interesting model for malleable tasks with continuous processor allotments by Prasanna and Musicus \cite{PrMu91,PrMu94,PrMu96}, we define two natural assumptions for malleable tasks: the processing time of any malleable task is non-increasing in the number of processors allotted, and the speedup is concave in the number of processors. We show that under these assumptions the work function of any malleable task is non-decreasing in the number of processors and is convex in the processing time. Furthermore, we propose a two-phase approximation algorithm for the scheduling problem. In the first phase we solve a linear program to obtain a fractional allotment for all tasks. By rounding the fractional solution, each malleable task is assigned a number of processors. In the second phase a variant of the list scheduling algorithm is employed. %In the phases we use two parameters $\mu\in\{1,\dots\lfloor (m+1)/2\rfloor\}$ and $\rho\in [0,1]$ for the allotment and the rounding, respectively, where $m$ is the number of processors. By choosing appropriate values of the parameters, we show (via a nonlinear program) that the approximation ratio of our algorithm is at most $100/63+100(\sqrt{6469}+13)/5481\approx 3.291919$. We also show that our result is asymptotically tight

Application of submodular optimization to single machine scheduling with controllable processing times subject to release dates and deadlines

In this paper, we study a scheduling problem on a single machine, provided that the jobs have individual release dates and deadlines, and the processing times are controllable. The objective is to find a feasible schedule that minimizes the total cost of reducing the processing times. We reformulate the problem in terms of maximizing a linear function over a submodular polyhedron intersected with a box. For the latter problem of submodular optimization, we develop a recursive decomposition algorithm and apply it to solving the single machine scheduling problem to achieve the best possible running time

Resource Allocation in Networked and Distributed Environments

A central challenge in networked and distributed systems is resource management: how can we partition the available resources in the system across competing users, such that individual users are satisfied and certain system-wide objectives of interest are optimized? In this thesis, we deal with many such fundamental and practical resource allocation problems that arise in networked and distributed environments. We invoke two sophisticated paradigms -- linear programming and probabilistic methods -- and develop provably-good approximation algorithms for a diverse collection of applications. Our main contributions are as follows. Assignment problems: An assignment problem involves a collection of objects and locations, and a load value associated with each object-location pair. Our goal is to assign the objects to locations while minimizing various cost functions of the assignment. This setting models many applications in manufacturing, parallel processing, distributed storage, and wireless networks. We present a single algorithm for assignment which generalizes many classical assignment schemes known in the literature. Our scheme is derived through a fusion of linear algebra and randomization. In conjunction with other ideas, it leads to novel guarantees for multi-criteria parallel scheduling, broadcast scheduling, and social network modeling. Precedence constrained scheduling: We consider two precedence constrained scheduling problems, namely sweep scheduling and tree scheduling, which are inspired by emerging applications in high performance computing. Through a careful use of randomization, we devise the first approximation algorithms for these problems with near-optimal performance guarantees. Wireless communication: Wireless networks are prone to interference. This prohibits proximate network nodes from transmitting simultaneously, and introduces fundamental challenges in the design of wireless communication protocols. We develop fresh geometric insights for characterizing wireless interference. We combine our geometric analysis with linear programming and randomization, to derive near-optimal algorithms for latency minimization and throughput capacity estimation in wireless networks. In summary, the innovative use of linear programming and probabilistic techniques for resource allocation, and the novel ways of connecting them with application-specific ideas is the pivotal theme and the focal point of this thesis

Solving Challenging Real-World Scheduling Problems

This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast