Scheduling with Concurrency-Based Constraints

This paper considers scheduling problems with timing constraints of the forms < (precedence), ≤ (no later than), and ≐ (concurrence). Scheduling unit-time jobs subject to < and ≐ constraints, and scheduling unit-time jobs subject to ≤ constraints, are proved NP-complete for fixed k ≥ 3 process...

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Bibliographic Details
Published in:Journal of algorithms Vol. 18; no. 1; pp. 98 - 123
Main Authors: Berger, B., Cowen, L.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 1995
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Exact sciences and technology
Software
Software engineering
Processor
Optimal algorithm
Constraint
Concurrency
NP complete problem
Scheduling
Timing
Parallelization
ISSN:0196-6774, 1090-2678
Online Access:Get full text
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Summary:This paper considers scheduling problems with timing constraints of the forms < (precedence), ≤ (no later than), and ≐ (concurrence). Scheduling unit-time jobs subject to < and ≐ constraints, and scheduling unit-time jobs subject to ≤ constraints, are proved NP-complete for fixed k ≥ 3 processors. (This contrasts with the case of just < constraints, which is a famous open problem.) We then show that a modified version of Gabow′s linear time 2-processor scheduling algorithm can optimally handle all three types of constraints. Linear time and NC algorithms for optimally scheduling with any subset of {<, ≤, ≐ } constraints are thus obtained for k = 2 processors. Approximation results for k ≥ 3 processors are also obtained. Finally, we consider a problem that arises in practice on the Tera architecture, proving an NP-completeness result and providing an approximation algorithm.
ISSN:0196-6774
1090-2678
DOI:10.1006/jagm.1995.1003