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90
On Multidimensional Packing Problems
, 1999
"... We study the approximability of multidimensional generalizations of the classical problems of multiprocessor scheduling, bin packing and the knapsack problem. Specifically, we study the vector scheduling problem, its dual problem, namely, the vector bin packing problem, and a class of packing integ ..."
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Cited by 98 (4 self)
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We study the approximability of multidimensional generalizations of the classical problems of multiprocessor scheduling, bin packing and the knapsack problem. Specifically, we study the vector scheduling problem, its dual problem, namely, the vector bin packing problem, and a class of packing integer programs. The vector scheduling problem is to schedule n ddimensional tasks on m machines such that the maximum load over all dimensions and all machines is minimized. The vector bin packing problem, on the other hand, seeks to minimize the number of bins needed to schedule all n tasks such that the maximum load on any dimension across all bins is bounded by a fixed quantity, say 1. Such problems naturally arise when scheduling multiple resource requirements. We obtain a
Toward a Theory of Transactional Contention Managers
 In Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC
, 2005
"... In recent software transactional memory proposals, a contention manager module is responsible for ensuring that the system as a whole makes progress. A number of contention manager algorithms have been proposed and empirically evaluated. In this paper we lay some foundations for a theory of contenti ..."
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Cited by 96 (14 self)
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In recent software transactional memory proposals, a contention manager module is responsible for ensuring that the system as a whole makes progress. A number of contention manager algorithms have been proposed and empirically evaluated. In this paper we lay some foundations for a theory of contention management. We present the greedy contention manager, the first to combine nontrivial provable properties with good practical performance. In a model where transaction delays are finite, the greedy manager guarantees that every transaction commits within a bounded time, and the time to complete n concurrent transactions that share s objects is within a factor of s(s + 1) + 2 of the time that would have been taken by an optimal offline list scheduler. No contention manager reviewed in the literature satisfies both the properties. Benchmark results convey our claim of the practicality of the greedy manager.
Parallel Query Processing
 ACM Computing Surveys
, 1993
"... With relations growing larger and queries becoming more complex, parallel query processing is an increasingly attractive option for improving the performance of database systems. The objective of this paper is to examine the various issues encountered in parallel query processing and the techniques ..."
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Cited by 75 (0 self)
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With relations growing larger and queries becoming more complex, parallel query processing is an increasingly attractive option for improving the performance of database systems. The objective of this paper is to examine the various issues encountered in parallel query processing and the techniques available for addressing these issues. The focus of the paper is on the join operation with both sortmerge join and hash joins being considered. Three types of parallelism can be exploited, namely intraoperator, interoperator, and interquery parallelism. In intraoperator parallelism the major issue is task creation, and the objective is to split a join operation into tasks in a manner such that the load can be spread evenly across a given number of processors. This is a challenge when the values on the join attribute are not uniformly distributed. Interoperator parallelism can be achieved either through parallel execution of independent operations or through pipelining. In either case,...
Application scheduling and processor allocation in multiprogrammed parallel processing systems
 Performance Evaluation
, 1994
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Improved scheduling algorithms for minsum criteria
 Automata, Languages and Programming, volume 1099 of Lecture Notes in Computer Science
, 1996
"... Abstract. We consider the problem of finding nearoptimal solutions for a variety of A/I)hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worstcase bounds in a number ..."
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Cited by 64 (18 self)
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Abstract. We consider the problem of finding nearoptimal solutions for a variety of A/I)hard scheduling problems for which the objective is to minimize the total weighted completion time. Recent work has led to the development of several techniques that yield constant worstcase bounds in a number of settings. We continue this line of research by providing improved performance guarantees for several of the most basic scheduling models, and by giving the first constant performance guarantee for a number of more realistically constrained scheduling problems. For example, we give an improved performance guarantee for minimizing the total weighted completion time subject to release dates on a single machine, and subject to release dates and/or precedence constraints on identical parallel machines. We also give improved bounds on the power of preemption in scheduling jobs with release dates on parallel machines. We give improved online algorithms for many more realistic scheduling models, including environments with parallelizable jobs, jobs contending for shared resources, tree precedenceconstrained jobs, as well as shop scheduling models. In several of these cases, we give the first constant performance guarantee achieved online. Finally, one of the consequences of our work is the surprising structural property that there are schedules that simultaneously approximate the optimal makespan and the optimal weighted completion time to within small constants. Not only do such schedules exist, but we can find approximations to them with an online algorithm. 1
On Chromatic Sums and Distributed Resource Allocation
"... This paper studies an optimization problem that arises in the context of distributed resource allocation: Given a conflict graph that represents the competition of processors over resources, we seek an allocation under which no two jobs with conflicting requirements are executed simultaneously. Our ..."
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Cited by 61 (10 self)
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This paper studies an optimization problem that arises in the context of distributed resource allocation: Given a conflict graph that represents the competition of processors over resources, we seek an allocation under which no two jobs with conflicting requirements are executed simultaneously. Our objective is to minimize the average response time of the system. In alternative formulation this is known as the Minimum Color Sum (MCS) problem [24]. We show, that the algorithm based on finding iteratively a maximum independent set (MaxIS) is a 4approximation to the MCS. This bound is tight to within a factor of 2. We give improved ratios for the classes of bipartite, boundeddegree, and line graphs. The bound generalizes to a 4aeapproximation of MCS for classes of graphs for which the maximum independent set problem can be approximated within a factor of ae. On the other hand, we show that an n1 \Gamma fflapproximation is NPhard, for some ffl? 0. For some instances of the resource allocation problem, such as the Dining Philosophers, an efficient solution requires edge coloring of the conflict graph. We introduce the Minimum Edge Color Sum (MECS) problem which is shown to be NPhard. We show that a 2approximation to MECS(G) can be obtained distributively using compact coloring within O(log² n) communication rounds.
Preemptive scheduling of parallel jobs on multiprocessors
 In SODA
, 1996
"... Abstract. We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within ..."
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Cited by 44 (3 self)
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Abstract. We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within 2 − 2 2 times the optimum. In other words, we prove a competitive ratio of 2 − n+1 n+1. The result is extended to jobs with multiple phases of parallelism (which can be used to model jobs with sublinear speedup) and to interactive jobs (with phases during which the job has no CPU requirements) to derive solutions guaranteed to be within 4 − 4 times the optimum. In comparison n+1 with previous work, our assumption that job execution times are unknown prior to their completion is more realistic, our multiphased job model is more general, and our approximation ratio (for jobs with a single phase of parallelism) is tighter and cannot be improved. While this work presents theoretical results obtained using competitive analysis, we believe that the results provide insight into the performance of practical multiprocessor scheduling algorithms that operate in the absence of complete information.
Fairness in Parallel Job Scheduling
, 2000
"... This paper introduces a new preemptive algorithm that is well suited for fair online scheduling of parallel jobs. Fairness is achieved by selecting job weights to be equal to the resource consumption of the job and by limiting the time span a job can be delayed by other jobs submitted after it. Fur ..."
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Cited by 35 (6 self)
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This paper introduces a new preemptive algorithm that is well suited for fair online scheduling of parallel jobs. Fairness is achieved by selecting job weights to be equal to the resource consumption of the job and by limiting the time span a job can be delayed by other jobs submitted after it. Further, the processing time of a job is not known when the job is released. It is proven that the algorithm achieves a constant competitive ratio for both the makespan and the weighted completion time for the given weight selection. Finally, the algorithm is also experimentally evaluated with the help of workload traces.
Lineartime Approximation Schemes for Scheduling Malleable Parallel Tasks
 Proceedings of the 10th Annual ACMSIAM Symposium on Discrete Algorithms
, 1999
"... A malleable parallel task is one whose execution time is a function of the number of (identical) processors alloted to it. We study the problem of scheduling a set of n independent malleable tasks on a xed number of parallel processors, and propose an approximation scheme that for any xed > 0, c ..."
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Cited by 35 (14 self)
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A malleable parallel task is one whose execution time is a function of the number of (identical) processors alloted to it. We study the problem of scheduling a set of n independent malleable tasks on a xed number of parallel processors, and propose an approximation scheme that for any xed > 0, computes in O(n) time a nonpreemptive schedule of length at most (1 + ) times the optimum. 1 Introduction In this paper, we study the following scheduling problem. Suppose there is given a set of tasks T = fT 0 ; : : : ; T n 1 g and a set of identical processors M = f1; : : : ; mg. Each task T j has an associated function t j : M ! Q + that gives the execution time t j (`) of task T j in terms of the number of processors ` 2 M that are assigned to T j . Given j processors alloted to task T j , these j processors are required to execute task T j in union and without preemption, i.e. they all have to start processing task T j at some starting time j , and complete it at j + t j (...
Scheduling parallelizable tasks to minimize average response time
 In 6th Annual ACM Symposium on Parallel Algorithms and Architectures
, 1994
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