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Optimal triangulation of large real world input-output matrices

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Abstract

In this paper we present optimum triangulations of a large number of input-output matrices. In particular, we report about a series of (44,44)-matrices of the years 1959, 1965, 1970, 1975 of the countries of the European Community, about all (56, 56)-matrices compiled by Deutsches Institut für Wirtschaftsforschung for the Federal Republic of Germany, and about the (60,60)-matrices of the Statistisches Bundesamt of the Federal Republic of Germany. These optimum triangulation were obtained with a code developed by the authors which utilizes new polyhedral results for the triangulation problem in a linear programming cutting plane framework. With this code the range of solvability of triangulation problems was more than doubled (in terms of sector numbers) compared to previous work. In particular, for none of the triangulation problems mentioned above optimum solutions were known before. Moreover, we discuss various claims about properties of optimum solutions made in the literature and question some common concepts of analysing triangulated input-output matrices.

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  1. Institut für Mathematik Lehrstuhl für Angewandte Mathematik II, Universität Augsburg, Memminger Str. 6, 8900, Augsburg, West Germany

    M. Grötschel, M. Jünger & G. Reinelt

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  1. M. Grötschel
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  2. M. Jünger
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  3. G. Reinelt
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Grötschel, M., Jünger, M. & Reinelt, G. Optimal triangulation of large real world input-output matrices. Statistische Hefte 25, 261–295 (1983). https://doi.org/10.1007/BF02932410

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  • DOI: https://doi.org/10.1007/BF02932410

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