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137
APPROXIMATION ALGORITHMS FOR SCHEDULING UNRELATED PARALLEL MACHINES
, 1990
"... We consider the following scheduling problem. There are m parallel machines and n independent.jobs. Each job is to be assigned to one of the machines. The processing of.job j on machine i requires time Pip The objective is to lind a schedule that minimizes the makespan. Our main result is a polynomi ..."
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Cited by 267 (6 self)
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We consider the following scheduling problem. There are m parallel machines and n independent.jobs. Each job is to be assigned to one of the machines. The processing of.job j on machine i requires time Pip The objective is to lind a schedule that minimizes the makespan. Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints. In contrast to our main result, we prove that no polynomial algorithm can achieve a worstcase ratio less than ~ unless P = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.
The Spring Kernel: A New Paradigm for RealTime Systems
 IEEE Software
, 1991
"... Next generation realtime systems will require greater flexibility and predictability than is commonly found in today's systems. These future systems include the space station, integrated vision/robotics/AI systems, collections of humans/robots coordinating to achieve common objectives (usuall ..."
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Cited by 210 (21 self)
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Next generation realtime systems will require greater flexibility and predictability than is commonly found in today's systems. These future systems include the space station, integrated vision/robotics/AI systems, collections of humans/robots coordinating to achieve common objectives (usually in hazardous environments such as undersea exploration or chemical plants), and various command and control applications. The Spring kernel is a research oriented kernel designed to form the basis of a flexible, hard realtime operating system for such applications. Our approach challenges several basic assumptions upon which most current realtime operating systems are built and subsequently advocates a new paradigm based on the notion of predictability and a method for online dynamic guarantees of deadlines. The Spring kernel is being implemented on a network of (68020 based) multiprocessors called SpringNet. 1
Scheduling algorithms and operating systems support for realtime systems
 PROCEEDINGS OF THE IEEE
, 1994
"... This paper summarizes the state of the realtime field in the areas of scheduling and operating system kernels. Given the vast amount of work that has been done by both the operations research and computer science communities in the scheduling area, we discuss four paradigms underlying the schedulin ..."
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Cited by 153 (1 self)
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This paper summarizes the state of the realtime field in the areas of scheduling and operating system kernels. Given the vast amount of work that has been done by both the operations research and computer science communities in the scheduling area, we discuss four paradigms underlying the scheduling approaches and present several exemplars of each. The four paradigms are: static tabledriven scheduling, static priority preemptive scheduling, dynamic planningbased scheduling, and dynamic best efSort scheduling. In the operating system context, we argue that most of the proprietary commercial kernels as well as realtime extensions to timesharing operating system kernels do not fit the needs of predictable realtime systems. We discuss several research kernels that are currently being built to explicitly meet the needs of realtime applications.
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 145 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Implications of Classical Scheduling Results For RealTime Systems
 IEEE COMPUTER
, 1995
"... Important classical scheduling theory results for realtime computing are identified. Implications of these results from the perspective of a realtime systems designer are discussed. Uniprocessor and multiprocessor results are addressed as well as important issues such as future release times, pre ..."
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Cited by 142 (1 self)
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Important classical scheduling theory results for realtime computing are identified. Implications of these results from the perspective of a realtime systems designer are discussed. Uniprocessor and multiprocessor results are addressed as well as important issues such as future release times, precedence constraints, shared resources, task value, overloads, static versus dynamic scheduling, preemption versus nonpreemption, multiprocessing anomalies, and metrics. Examples of what scheduling algorithms are used in actual applications are given.
Models of Machines and Computation for Mapping in Multicomputers
, 1993
"... It is now more than a quarter of a century since researchers started publishing papers on mapping strategies for distributing computation across the computation resource of multiprocessor systems. There exists a large body of literature on the subject, but there is no commonlyaccepted framework ..."
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Cited by 86 (1 self)
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It is now more than a quarter of a century since researchers started publishing papers on mapping strategies for distributing computation across the computation resource of multiprocessor systems. There exists a large body of literature on the subject, but there is no commonlyaccepted framework whereby results in the field can be compared. Nor is it always easy to assess the relevance of a new result to a particular problem. Furthermore, changes in parallel computing technology have made some of the earlier work of less relevance to current multiprocessor systems. Versions of the mapping problem are classified, and research in the field is considered in terms of its relevance to the problem of programming currently available hardware in the form of a distributed memory multiple instruction stream multiple data stream computer: a multicomputer.
COMPLEXITY RESULTS FOR BANDWIDTH MINIMIZATION
, 1978
"... We present a lineartime algorithm for sparse symmetric matrices which converts a matrix into pentadiagonal form ("bandwidth 2"), whenever it is possible to do so using simultaneous row and column permutations. On the otherhand when an arbitrary integer k and graph G are given, we show tha ..."
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Cited by 85 (1 self)
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We present a lineartime algorithm for sparse symmetric matrices which converts a matrix into pentadiagonal form ("bandwidth 2"), whenever it is possible to do so using simultaneous row and column permutations. On the otherhand when an arbitrary integer k and graph G are given, we show that it is NPcomplete to determine whether or not there exists an ordering of the vertices such that the adjacency matrix has bandwidth<k, even when G is restricted to the class of free trees with all vertices of degree<3. Related problems for acyclic directed graphs (upper triangular matrices) are also discussed.
Twoprocessor scheduling with starttimes and deadlines
 SIAM Journal on Computing
, 1977
"... Abstract. Given a set 3 = {T1, T2, , T,} of tasks, each T/having execution time 1, an integer starttime si>0 and adeadlinedi> 0, alongwithprecedence constraintsamongthe tasks,weexamine the problem of determining whether there exists a schedule on two identical processors that executes each ..."
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Cited by 79 (0 self)
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Abstract. Given a set 3 = {T1, T2, , T,} of tasks, each T/having execution time 1, an integer starttime si>0 and adeadlinedi> 0, alongwithprecedence constraintsamongthe tasks,weexamine the problem of determining whether there exists a schedule on two identical processors that executes each task in the time intervalbetween its starttimeand deadline.We present an O(n3) algorithm that constructs such a schedule whenever one exists. The algorithm may also be used in a binary search mode to find the shortest such schedule or to find a schedule that minimizesmaximum &quot;tardiness&quot;.A number of natural extensions of this problem are seen to be NPcomplete and hence probably intractable. Key words, multiprocessing systems, scheduling algorithms, NPcomplete problems 1. Introduction. Since publication of the book Theory ofScheduling [4] by Conway, Maxwell, andMiller in 1967, considerableprogresshasbeenmade inthe mathematical analysis of abstract multiprocessing systems. One combinatorial model which is central to much of this work consists of a numberm of identical, independent processors, a finite set {T1, T2, Tn} of tasks to be executed,
Scheduling Hard RealTime Systems: A Review
, 1991
"... Recent results in the application of... this paper. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. Issues covered include uniprocessor and multiprocessor systems, periodic and aperiodic processes, static and dynamic algor ..."
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Cited by 59 (7 self)
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Recent results in the application of... this paper. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. Issues covered include uniprocessor and multiprocessor systems, periodic and aperiodic processes, static and dynamic algorithms, transient overloads and resource usage. Protocols that limit and reduce blocking are discussed. Considerations are also given to scheduling Ada tasks.
Tetris is Hard, Even to Approximate
 COCOON
, 2003
"... In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row. ..."
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Cited by 46 (2 self)
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In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row. We prove that in the o#ine version of Tetris, it is NPcomplete to maximize the number of cleared rows, maximize the number of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize the number of pieces placed before the game ends. We furthermore show the extreme inapproximability of the first and last of these objectives to within a factor of p , when given a sequence of p pieces, and the inapproximability of the third objective to within a factor of 2#, for any # > 0. Our results