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Multidimensional scaling is the problem of representing n objects: geometrically by n points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically(More)
Several years ago a typewritten translation (of obscure origin) of [l] raised some interest. This paper is devoted to the following theorem: If a (finite) connected graph has a positive real number attached to each edge (the length of the edge), and if these lengths are all distinct, then among the spanning1 trees (German: Gerüst) of the graph there is only(More)
We describe the numerical methods required in our approach to multi-dimensional scaling. The rationale of this approach has appeared previously. 1. Introduction We describe a numerical method for multidimensional scaling. In a companion paper [7] we describe the rationale for our approach to scaling, which is related to that of Shepard [9]. As the numerical(More)
KYST is an extremely flexible and portable computer program for multidimensional scaling and unfolding. It represents a merger of M-D-SCAL 5M and TORSCA 9, including the best features of both, as well as some new features of interest. The name, pronounced "kissed", is formed from the initials Kruskal, Young, Shepard, and Torgerson. This instruction manual(More)
On the background of Bor uvka's pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper Graham-Hell GH] by a few remarks and provide an update of the extensive literature devoted to this problem. In the contemporary terminology the Minimum Spanning Tree problem can be(More)