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The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates
 Discrete Applied Mathematics
, 1993
"... This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an Earliest Due Date first algorithm pro ..."
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Cited by 9 (2 self)
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This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an Earliest Due Date first algorithm provides an optimal nonpreemptive schedule for unitexecution time (UET) tasks, then the preemptive priority scheduling algorithm, referred to as Smallest Laxity First, provides an optimal preemptive schedule for realexecutiontime (RET) tasks. When the objective is to minimize the makespan, we get the same kind of result between Highest Level First schedules solving nonpreemptive tasks with UET and the Longest Remaining Path first schedule for the corresponding preemptive scheduling problem with RET tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained. Keywords: Preemptive Scheduling, List Schedule, Priority Schedule, Variable P...
Stochastic Scheduling with Variable Profile and Precedence Constraints
 STOCHASTIC SCHEDULING WITH VARIABLE PROFILE 187
, 1991
"... In this paper, we consider the stochastic profile scheduling problem of a partially ordered set of tasks on uniform processors. The set of available processors varies in time. The running times of the tasks are independent random variables with exponential distributions. We obtain a sufficient condi ..."
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Cited by 5 (3 self)
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In this paper, we consider the stochastic profile scheduling problem of a partially ordered set of tasks on uniform processors. The set of available processors varies in time. The running times of the tasks are independent random variables with exponential distributions. We obtain a sufficient condition under which a list policy stochastically minimizes the makespan within the class of preemptive policies. This result allows us to obtain a simple optimal policy when the partial order is an interval order, or an inforest, or an outforest. Keywords: Stochastic Scheduling, Profile Scheduling, Makespan, Precedence Constraint, Interval Order, InForest, OutForest, Uniform Processors, Stochastic Ordering. 1 Introduction Consider the following scheduling problem. We are given a set of tasks to be run in a system consisting of uniform processors (i.e., processors having different speeds). The executions of these tasks must satisfy some precedence constraints which are described by a dire...
Profile Scheduling by List Algorithms
, 1994
"... The notion of profile scheduling was first introduced by Ullman in 1975 in the complexity analysis of deterministic scheduling algorithms. In such a model, the number of processors available to a set of tasks may vary in time. Since the last decade, this model has been used to deal with systems subj ..."
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Cited by 2 (1 self)
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The notion of profile scheduling was first introduced by Ullman in 1975 in the complexity analysis of deterministic scheduling algorithms. In such a model, the number of processors available to a set of tasks may vary in time. Since the last decade, this model has been used to deal with systems subject to processor failures, multiprogrammed systems, or dynamically reconfigured systems. The aim of this paper is to overview optimal polynomial solutions for scheduling a set of partially ordered tasks in these systems. Particular attentions are given to a class of algorithms referred to as list scheduling algorithms. The objective of the scheduling problem is to minimize either the maximum lateness or the makespan. Results on preemptive and nonpreemptive deterministic scheduling, and on preemptive stochastic scheduling, are presented.
Makespan Minimization of Task Graphs with Random Task Running Times
 In Interconnection Networks and Mapping and Scheduling Parallel Computations, D. F. Hsu et al. (Eds.), AMS, DIMACS series
, 1994
"... . The problem of scheduling a set of tasks on two parallel and identical processors is considered. The executions of tasks are constrained by precedence relations. The running times of the tasks are independent random variables with a common exponential distribution. The goal of scheduling is to min ..."
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. The problem of scheduling a set of tasks on two parallel and identical processors is considered. The executions of tasks are constrained by precedence relations. The running times of the tasks are independent random variables with a common exponential distribution. The goal of scheduling is to minimize the makespan, i.e. the maximum task completion time. A simple optimal preemptive policy is proven to stochastically minimize the makespan when the precedence graph belongs to a class of forestcut graphs. 1. Introduction Parallel programs are usually represented by task graphs which are directed acyclic graphs where vertices represent tasks and arcs represent precedence relations between tasks. The executions of these tasks have to satisfy these precedence constraints in such a way that a task can start execution only when all its predecessor tasks have completed execution. For any given task graph, the scheduling problem consists in assigning tasks to a set of processors in such a wa...