Angewandte Mathematik Und Informatik Universit at Zu K Oln Traveling the Boundary of Minkowski Sums Ss Andor P.fekete Center for Parallel Computing Universitt at Zu Kk Oln D{50923 Kk Oln Germany
نویسنده
چکیده
We consider the problem of traveling the contour of the set of all points that are within distance 1 of a connected planar curve arrangement P, forming an embedding of the graph G. We show that if the overall length of P is L, there is a closed roundtrip that visits all points of the contour and has length no longer than 2L + 2. This result carries over in a more general setting: if R is a compact convex shape with interior points and boundary length`, we can travel the boundary of the Minkowski sum P R on a closed roundtrip no longer than 2L + `.
منابع مشابه
Angewandte Mathematik Und Informatik Universit at Zu K Oln Tree Spanners in Planar Graphs Ss Andor P. Fekete Center for Parallel Computing Universitt at Zu Kk Oln D{50923 Kk Oln Germany
A tree t-spanner of a graph G is a spanning subtree T of G in which the distance between every pair of vertices is at most t times their distance in G. Spanner problems have received some attention, mostly in the context of communication networks. It is known that for general unweighted graphs, the problem of deciding the existence of a tree t-spanner can be solved in polynomial time for t = 2,...
متن کاملAngewandte 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
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 \minimu...
متن کاملAngewandte Mathematik Und Informatik Universit at Zu K Oln Parallel Turbulence Simulation Based on Mpi
متن کامل