NP-completeness of linearly-connected multiprocessor scheduling
Book
·
OSTI ID:5090885
This paper analyzes the computational complexity of scheduling for linearly-connected multiprocessor architectures. A program to be scheduled is specified by a directed acyclic graph (DAG), where each vertex of the DAG represents a unit time operation to be performed by one of a fixed number of processors, and each arc of the DAG represents a precedence constraint. Each vertex must be assigned a start time and a processor such that all operations are completed and the constraints imposed by the DAG and the architecture are observed. A scheduling algorithm is a decision procedure to determine whether a given number of time units is sufficient for completion of the operations specified by a given DAG. The authors first show how precedence-constrained scheduling and linearly-connected multiprocessor scheduling can be expressed as subgraph isomorphism problems. They then specify another type of linearly-connected multiprocessor scheduling problem in terms of subgraph isomorphism and prove that it is NP-complete. Finally, they use similar techniques to prove that scheduling for the Aspex Inc. PIPE machine is NP-complete. The NP-completeness results support the development of approximation algorithms and heuristic methods for linearly-connected multiprocessor scheduling.
- OSTI ID:
- 5090885
- Country of Publication:
- United States
- Language:
- English
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