How the structure of precedence constraints may change the complexity class of scheduling problems

This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. We also show that there still are many very exciting challenges in this research area

Feasibility Tests for Recurrent Real-Time Tasks in the Sporadic DAG Model

A model has been proposed in [Baruah et al., in Proceedings of the IEEE Real-Time Systems Symposium 2012] for representing recurrent precedence-constrained tasks to be executed on multiprocessor platforms, where each recurrent task is modeled by a directed acyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and have to be completed within some specified relative deadline. The task may release jobs in this manner an unbounded number of times, with successive releases occurring at least the specified period apart. The feasibility problem is to determine whether such a recurrent task can be scheduled to always meet all deadlines on a specified number of dedicated processors. The case of a single task has been considered in [Baruah et al., 2012]. The main contribution of this paper is to consider the case of multiple tasks. We show that EDF has a speedup bound of 2-1/m, where m is the number of processors. Moreover, we present polynomial and pseudopolynomial schedulability tests, of differing effectiveness, for determining whether a set of sporadic DAG tasks can be scheduled by EDF to meet all deadlines on a specified number of processors

A Survey of Pipelined Workflow Scheduling: Models and Algorithms

International audienceA large class of applications need to execute the same workflow on different data sets of identical size. Efficient execution of such applications necessitates intelligent distribution of the application components and tasks on a parallel machine, and the execution can be orchestrated by utilizing task-, data-, pipelined-, and/or replicated-parallelism. The scheduling problem that encompasses all of these techniques is called pipelined workflow scheduling, and it has been widely studied in the last decade. Multiple models and algorithms have flourished to tackle various programming paradigms, constraints, machine behaviors or optimization goals. This paper surveys the field by summing up and structuring known results and approaches

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

Parameterized Complexity of Scheduling Chains of Jobs with Delays

In this paper, we consider the parameterized complexity of the following scheduling problem. We must schedule a number of jobs on m machines, where each job has unit length, and the graph of precedence constraints consists of a set of chains. Each precedence constraint is labelled with an integer that denotes the exact (or minimum) delay between the jobs. We study different cases; delays can be given in unary and in binary, and the case that we have a single machine is discussed separately. We consider the complexity of this problem parameterized by the number of chains, and by the thickness of the instance, which is the maximum number of chains whose intervals between release date and deadline overlap. We show that this scheduling problem with exact delays in unary is W[t]-hard for all t, when parameterized by the thickness, even when we have a single machine (m = 1). When parameterized by the number of chains, this problem is W[1]-complete when we have a single or a constant number of machines, and W[2]-complete when the number of machines is a variable. The problem with minimum delays, given in unary, parameterized by the number of chains (and as a simple corollary, also when parameterized by the thickness) is W[1]-hard for a single or a constant number of machines, and W[2]-hard when the number of machines is variable. With a dynamic programming algorithm, one can show membership in XP for exact and minimum delays in unary, for any number of machines, when parameterized by thickness or number of chains. For a single machine, with exact delays in binary, parameterized by the number of chains, membership in XP can be shown with branching and solving a system of difference constraints. For all other cases for delays in binary, membership in XP is open

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe