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A set covering formulation of the matrix equipartition problem

  • Sara Nicoloso
  • Paolo Nobili
II Mathematical Programming II.2 Discrete Optimization
  • 104 Downloads
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)

Abstract

This paper is concerned with a certain matrix decomposition problem which has been shown to be NP-hard (MATRIX EQUIPARTITION). Given a (0, 1)-matrix M with row-set R, MATRIX EQUIPARTITION consists in finding two equicardinality subsets R 1 and R 2 of R with maximum size, such that every row of R 1 is disjoint from every row of R 2. In addition to its theoretical significance, the problem arises also in applicative contexts like, for example, the design of Very Large Scale Integrated circuits (VLSI-design) and Flexible Manufacturing Systems (FMS). We prove that MATRIX EQUIPARTITION admits a Set Covering formulation. Although such formulation contains exponentially many constraints, it is easy to check implicitly whether a (0, 1)-vector satisfles all of them and, if not, to generate a set of violated constraints from the formulation. Such property is used to design an incremental algorithm to solve the problem to optimality. We tested the algorithm on several test problems and compared it to a standard Branch & Bound strategy.

Keywords

Boolean Function Flexible Manufacture System Incremental Algorithm Incidence Vector Programme Logic Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Sara Nicoloso
    • 1
  • Paolo Nobili
    • 1
  1. 1.Istituto di Analisi dei Sistemi ed Informatica del CNRRomaItaly

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