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.
References
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.
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).
C. McDiarmid, “Integral decomposition in polyhedra”, Mathematical Programming 25 (1983) 183–198.
D. de Werra, “A decomposition property of polyhedra”, to appear in Mathematical Programming.
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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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