Angewandte Mathematik Und Informatik Universit at Zu K Oln on Maximum Matchings and Minimum Stars Ss Andor P. Fekete Center for Parallel Computing Universitt at Zu Kk Oln D{50923 Kk Oln Germany
نویسنده
چکیده
We discuss properties and values of maximum matchings and minimum median problems for nite point sets. In particular, we consider \minimum stars", which are deened by a choosing a center, such that the total geometric distance to all the points in the set is minimized. Since the center point is not required to be an element of the set (i. e., the center may be a Steiner point), we get a \minimum Steiner star", of total length kminStStk. As a consequence of triangle inequality, the total length kmaxM atk of any maximum matching is a lower bound for the length kminStStk of a minimum Steiner star, which makes this ratio interesting in the context of optimal communication networks. The ratio also appears as the duality gap in an integer programming formulation of a location problem by Tamir and Mitchell. In this paper, we show that for an even set of points in the plane and Euclidean distances, the ratio kminStStk kmaxMatk cannot exceed 2 p 3. This proves a conjecture of Suri, who gave an example where this bound is achieved. We also give results for the case where distances are measured according to the Manhattan metric, extending some observations by Tamir and Mitchell.
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We discuss properties and values of maximum matchings and minimum median problems for nite point sets. In particular, we consider \minimum stars", which are deened by a center chosen from the given point set, such that the total geometric distance min kStk to all the points in the set is minimized. If the center point is not required to be an element of the set (i. e., the center may be a Stein...
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