“Product Partition” and related problems of scheduling and systems reliability: Computational complexity and approximation

Problem Product Partition differs from the NP-complete problem Partition in that the addition operation is replaced by the multiplication operation. Furthermore it differs from the NP-complete problem Subset Product in that it does not contain the product value B in its input. We prove that problem...

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Bibliographic Details
Published in:European journal of operational research Vol. 207; no. 2; pp. 601 - 604
Main Authors: Ng, C.T., Barketau, M.S., Cheng, T.C.E., Kovalyov, Mikhail Y.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.12.2010
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Approximation
Complexity theory
Complexity theory Scheduling Subset Product FPTAS Systems reliability
Computation
Exact sciences and technology
FPTAS
Mathematical analysis
Multiplication
Operational research
Operational research and scientific management
Operational research. Management science
Optimization
Optimization techniques
Partitions
Reliability
Reliability theory. Replacement problems
Scheduling
Scheduling, sequencing
Studies
Subset Product
System reliability
Systems reliability
Systems reliability
Scheduling
Complexity theory
FPTAS
Subset Product
Partition
Multiplication
Polynomial approximation
Processing time
Series system
Approximation algorithm
System reliability
Computational complexity
Optimization
Polynomial time
Time dependence
NP hard problem
NP complete problem
Execution time
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:Problem Product Partition differs from the NP-complete problem Partition in that the addition operation is replaced by the multiplication operation. Furthermore it differs from the NP-complete problem Subset Product in that it does not contain the product value B in its input. We prove that problem Product Partition and several of its modifications are NP-complete in the strong sense. Our results imply the strong NP-hardness of a number of scheduling problems with start-time-dependent job processing times and a problem of designing a reliable system with a series–parallel structure. It should be noticed that the strong NP-hardness of the considered optimization problems does not preclude the existence of a fully polynomial time approximation scheme (FPTAS) for them. We present a simple FPTAS for one of these problems.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.05.034