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The Algorithmic Complexity of Modular Decomposition

Author

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  • Bioch, J.C.

Abstract

Modular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. We propose an O(mn)-algorithm for the recognition of a modular set of a monotone Boolean function f with m prime implicants and n variables. Using this result we show that the computation of the modular closure of a set can be done in time O(mn2). On the other hand, we prove that the recognition problem for general Boolean func tions is NP-complete. Moreover, we introduce the so called generalized Shannon decomposition of a Boolean functions as an efficient tool for proving theorems on Boolean function decompositions.

Suggested Citation

  • Bioch, J.C., 2001. "The Algorithmic Complexity of Modular Decomposition," ERIM Report Series Research in Management ERS-2001-30-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:99
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    More about this item

    Keywords

    Boolean functions; computational complexity; decomposition algorithm; modular decomposition; substitution decomposition;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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