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Variations on the integral decomposition property

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Netflow at Pisa

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 26))

Abstract

Besides the integral decomposition property of polyhedra, a ‘fractional’ (or ‘real’) decomposition property may be stated. Some classes of polyhedra for which these properties hold are described. One shows that both types of decompositions are used in some scheduling problems: while the integral decomposition property is applicable to timetabling, the fractional decomposition is mainly used in solving some types of scheduling problems on parallel processors.

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References

  1. S. Baum and L.E. Trotter, “Integral rounding and polyhedral decomposition of totally unimodular systems”, in: R. Henn, B. Korte and W. Oettli, eds., Optimization and operations research, Lecture Notes in Economics and Mathematical Systems 157 (Springer-Verlag, Berlin, 1977) pp. 25–33.

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  2. J. Blazewicz, W. Cellary, R. Slowinski and J. Weglarz, “Deterministic problems of scheduling tasks on parallel processors”, Podstawy Sterowania 6 (1976) 155–178 (in Polish).

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  3. C. McDiarmid, “Integral decomposition in polyhedra”, Mathematical Programming 25 (1983) 183–198.

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  4. D. de Werra, “A decomposition property of polyhedra”, to appear in Mathematical Programming.

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Giorgio Gallo Claudio Sandi

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© 1986 The Mathematical Programming Society, Inc.

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de Werra, D. (1986). Variations on the integral decomposition property. In: Gallo, G., Sandi, C. (eds) Netflow at Pisa. Mathematical Programming Studies, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121093

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  • DOI: https://doi.org/10.1007/BFb0121093

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00922-8

  • Online ISBN: 978-3-642-00923-5

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