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Flow and Stretch Metrics for Scheduling Continuous Job Streams
 In Proceedings of the 9th Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... this paper, we isolate and study the problem of scheduling a continuous stream of requests of varying sizes. More precisely, assume a request or job j has ..."
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Cited by 146 (9 self)
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this paper, we isolate and study the problem of scheduling a continuous stream of requests of varying sizes. More precisely, assume a request or job j has
On Multidimensional Packing Problems
 TENTH ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 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 96 (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 tasks that have multiple resource requirements. We obtain a variety of new algorithmic as well as inapproximability results for these problems. For vector scheduling, we give a PTAS when d is a fixed constant, and an O(minflog dm; log 2 dg)approximation in gen...
Approximation Techniques for Average Completion Time Scheduling
, 1997
"... We consider the problem of nonpreemptive scheduling to minimize average (weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constantfactor approximations for this problem, based on solving a preemptive or linear programming ..."
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Cited by 92 (7 self)
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We consider the problem of nonpreemptive scheduling to minimize average (weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constantfactor approximations for this problem, based on solving a preemptive or linear programming relaxation and then using the solution to get an ordering on the jobs. We introduce several new techniques which generalize this basic paradigm. We use these ideas to obtain improved approximation algorithms for onemachine scheduling to minimize average completion time with release dates. In the process, we obtain an optimal randomized online algorithm for the same problem that beats a lower bound for deterministic online algorithms. We consider extensions to the case of parallel machine scheduling, and for this we introduce two new ideas: first, we show that a preemptive onemachine relaxation is a powerful tool for designing parallel machine scheduling algorithms that simultaneously pro...
Anomalies in Parallel BranchandBound Algorithms
, 1984
"... We consider the effects of parallelizing branchandbound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branchandbound algorithm using n 2 processors to take more time than one using n 1 processors even though n 1 < n 2 . Further ..."
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Cited by 66 (3 self)
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We consider the effects of parallelizing branchandbound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branchandbound algorithm using n 2 processors to take more time than one using n 1 processors even though n 1 < n 2 . Furthermore, it is also possible to achieve speedups that are in excess of the ratio n 2 /n 1 . Experimental results with the 0/1Knapsack and Traveling Salesperson problems are also presented.
Experimental evaluation of heuristic optimization algorithms: A tutorial
 Journal of Heuristics
, 2001
"... Heuristic optimization algorithms seek good feasible solutions to optimization problems in circumstances where the complexities of the problem or the limited time available for solution do not allow exact solution. Although worst case and probabilistic analysis of algorithms have produced insight on ..."
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Cited by 46 (0 self)
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Heuristic optimization algorithms seek good feasible solutions to optimization problems in circumstances where the complexities of the problem or the limited time available for solution do not allow exact solution. Although worst case and probabilistic analysis of algorithms have produced insight on some classic models, most of the heuristics developed for large optimization problem must be evaluated empirically—by applying procedures to a collection of specific instances and comparing the observed solution quality and computational burden. This paper focuses on the methodological issues that must be confronted by researchers undertaking such experimental evaluations of heuristics, including experimental design, sources of test instances, measures of algorithmic performance, analysis of results, and presentation in papers and talks. The questions are difficult, and there are no clear right answers. We seek only to highlight the main issues, present alternative ways of addressing them under different circumstances, and caution about pitfalls to avoid. Key Words: Heuristic optimization, computational experiments 1.
Profiledriven instruction level parallel scheduling with application to super blocks
 In Intern. Symposium on Microarchitecture (MICRO
, 1996
"... VLIW scheduling, profile driven scheduling, superblocks, hyperblocks Code scheduling to exploit instruction level parallelism (lLP) is a central problem in compiler optimization research, in light of the increased use of longinstructionword computers. Unfortunately, optimum scheduling is computati ..."
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Cited by 41 (3 self)
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VLIW scheduling, profile driven scheduling, superblocks, hyperblocks Code scheduling to exploit instruction level parallelism (lLP) is a central problem in compiler optimization research, in light of the increased use of longinstructionword computers. Unfortunately, optimum scheduling is computationally intractable, and one must resort to carefully crafted heuristics in practice. Ifthe scope of application of a scheduling heuristic is limited to basic blocks, considerable performance loss may be incurred at block boundaries. To overcome this obstacle, basic blocks are coalesced across branches to form either superblocks or hyperblocks, with the branches labeled with branch probabilities obtained via profiling. Then, the goal of the scheduling heuristic is to minimize the expected completion time of the superblock or the hyperblock. In this paper, we analyze the general problem of scheduling with profIle information and present some experimental results on heuristics that are suggested by our analysis. Specifically, we carry out a theoretical analysis on a simplified abstraction of the problem to obtain insight into its structure, and to develop provably good algorithms. Based on the theoretical analysis of the simplified abstraction, we develop a generic scheme for converting any list scheduling heuristic for basic blocks into a heuristic for the superblockslhyperblocks with associated profIle information. Our techniques are applicable to the general case of scheduling on piplined heterogeneous units with unequal latencies. Experiments show that our scheme offers substantial performance improvement over critical path scheduling on a range of benchmark inputs and machine models.
OnLine Scheduling  A Survey
, 1997
"... Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequ ..."
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Cited by 39 (0 self)
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Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequence of jobs that have to be processed on the machines available to us. In the most basic problem, each job is characterized by its running time and has to be scheduled for that time on one of the machines. In other variants there may be additional restrictions or relaxations specifying which schedules are allowed. We want to schedule the jobs as efficiently as possible, which most often means that the total length of the schedule (the makespan) should be as small as possible, but other objective functions are also considered. The notion of an online algorithm is intended to formalize the realistic scenario, where the algorithm does not have the access to the whole inp...
Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines
, 1999
"... We give a polynomial approximation scheme for the problem of scheduling on uniformly related parallel machines for a large class of objective functions that depend only on the machine completion times, including minimizing the l p norm of the vector of completion times. This generalizes and simp ..."
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Cited by 38 (8 self)
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We give a polynomial approximation scheme for the problem of scheduling on uniformly related parallel machines for a large class of objective functions that depend only on the machine completion times, including minimizing the l p norm of the vector of completion times. This generalizes and simplifies many previous results in this area. 1 Introduction Scheduling is one of fundamental areas of combinatorial optimization. Most multiprocessor scheduling problems are known to be hard to solve optimally (NPhard, see below). Thus the research focuses on giving efficient approximation algorithms that produce a solution close to the optimal one. Ideally, one hopes to obtain a family of polynomial algorithms such that for any given " ? 0 the corresponding algorithm is guaranteed to produce a solution with a cost within a factor of (1 + ") of the optimum cost; such a family is called a polynomial approximation scheme. A polynomial scheme for the basic problem of minimization of the total...
Online scheduling
 ONLINE ALGORITHMS, LECTURE NOTES IN COMPUTER SCIENCE 1442
, 1998
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Resource Scheduling for Parallel Database and Scientific Applications
 in Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms and Architectures
, 1996
"... We initiate a study of resource scheduling problems in parallel database and scientific applications. Based on this study we formulate a problem. In our formulation, jobs specify their running times and amounts of a fixed number of other resources (like memory, IO) they need. The resourcetime trade ..."
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Cited by 32 (5 self)
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We initiate a study of resource scheduling problems in parallel database and scientific applications. Based on this study we formulate a problem. In our formulation, jobs specify their running times and amounts of a fixed number of other resources (like memory, IO) they need. The resourcetime tradeoff may be fundamentally different for different resource types. The processor resource is malleable, meaning we can trade processors for time gracefully. Other resources may not be malleable. One way to model them is to assume no malleability: the entire requirement of those resources has to be reserved for a job to begin execution, and no smaller quantity is acceptable. The jobs also have precedences amongst them; in our applications, the precedence structure may be restricted to being a collection of trees or seriesparallel graphs. Not much is known about considering precedence and nonmalleable resource constraints together. For many other problems, it has been possible to find schedule...