Jünger, Michael and Grötschel, Martin and Reinelt, Gerhard
(1984)
Optimal Triangulation of Large Real World input- output Matrices.
Published in:
Statistische Hefte (25).
pp. 261-295.
Abstract
In this paper we present optimum triangulations of a large number of inputoutput
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 fHr
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 triangulations 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 solu
tions made in the literature and question some common concepts of analysing
triangulated input-output matrices.
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