NP-complete scheduling problems

Ullman, Jeffrey D.

doi:10.1016/s0022-0000(75)80008-0

Cited by 1,173 publications

(435 citation statements)

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“…With regular precedence-constraints, many problems are known to be NP-hard even if jobs have unit-length or if the precedence-constraints have limited topologies. For example, P |p i = 1, prec|C max is NP-hard [22], as well as P |p i = 1, prec| ∑ C j [18]. These hardness results are not valid for selfish precedence-constraints.…”

Section: Selfish Precedence-constraints Of Unit-length Jobsmentioning

confidence: 96%

Scheduling with Bully Selfish Jobs

Tamir

2010

Lecture Notes in Computer Science

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In job scheduling with precedence constraints, i ≺ j means that job j cannot start being processed before job i is completed. In this paper we consider selfish bully jobs who do not let other jobs start their processing if they are around. Formally, we define the selfish precedenceconstraint where i ≺ s j means that j cannot start being processed if i has not started its processing yet. Interestingly, as was detected by a devoted kindergarten teacher whose story is told below, this type of precedence constraints is very different from the traditional one, in a sense that problems that are known to be solvable efficiently become NP-hard and vice-versa.The work of our hero teacher, Ms. Schedule, was initiated due to an arrival of bully jobs to her kindergarten. Bully jobs bypass all other nice jobs, but respect each other. This natural environment corresponds to the case where the selfish precedence-constraints graph is a complete bipartite graph. Ms. Schedule analyzed the minimum makespan and the minimum total flow-time problems for this setting. She then extended her interest to other topologies of the precedence constraints graph and other special instances with uniform length jobs and/or release times.

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Section: Selfish Precedence-constraints Of Unit-length Jobsmentioning

confidence: 96%

Scheduling with Bully Selfish Jobs

Tamir

2010

Lecture Notes in Computer Science

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“…Task scheduling and schedulability analysis have been intensively studied for the past decades, one of the reasons being the high complexity of the targeted problems [Ull75], [Sta94]. The reader is referred to [Aud95] and [Bal98] for surveys on this topic.…”

Section: Scheduling and Schedulability Analysis Of Real-time Systemsmentioning

confidence: 99%

Analysis and Optimisation of Hierarchically Scheduled Multiprocessor Embedded Systems

Pop

Eles

et al. 2007

Int J Parallel Prog

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“…Optimal execution of software tasks on a parallel system requires multiprocessor task scheduling [Lin and Chen 1996] which is a known NPcomplete problem [Ullman 1975], hence it is concluded that AOGPP system cosynthesis is at least NP-hard.…”

Section: Cosynthesis Problem Formulationmentioning

confidence: 99%

Cmaps

Hsiung

2000

ACM Trans. Des. Autom. Electron. Syst.

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Currently, a lot of research is devoted to system design, and little work is done on requirements analysis. Besides going from specification to design, one of our main objectives is to show how an application problem can be transformed into specifications. Working from the hardwaresoftware codesign perspective, a system is designed starting from an application problem itself, rather than the detailed behavioral specifications. Given an application problem specified as a directed acyclic graph of elementary problems, a hardware-software solution is derived such that the synthesized software, a parallel pseudoprogram, can be scheduled and executed on the synthesized hardware, a set of system-level parallel computer specifications, with heuristically optimal performance. This is known as system-level cosynthesis of application-oriented general-purpose parallel systems for which a novel methodology called Cosynthesis Methodology for Application-Oriented Parallel Systems (CMAPS), is presented. Since parallel programs and multiprocessor architectures are largely interdependent, CMAPS explores the relationship between hardware designs and software algorithms by interleaving the modeling phases and the synthesis phases of both hardware and software. High scalability in terms of problem complexity and easy upgradability to new technologies are achieved through modularization of the input problem specification, of the software algorithms, and of the hardware subsystem models. The work presented in this paper will be beneficial to designers of general-purpose parallel computer systems which must be oriented toward solving some user-specified problem such as the global controller of an industry automation process or a multiprocessor video server. Some application examples are given to illustrate various codesign phases of CMAPS and its feasibility.

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NP-complete scheduling problems

Cited by 1,173 publications

References 5 publications

Scheduling with Bully Selfish Jobs

Scheduling with Bully Selfish Jobs

Analysis and Optimisation of Hierarchically Scheduled Multiprocessor Embedded Systems

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