Search

This paper investigates geometric and algorithmic properties of the Voronoi diagram for a transportation network on the Euclidean plane. In the presence of a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm2 + m3 + nm log n) algorithm to compute the Voronoi diagram for a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network. Moreover, in the case that the roads in a transportation network have only a constant number of directions and speeds, we propose two algorithms; one needs O(nm + m2 + n log n) time with O(m(n + m)) space and the other O(nm log n + m2log m) time with O(n + m) space. [ABSTRACT FROM AUTHOR]

We study the Hausdorff Voronoi diagram of a set 5 of polygonal objects in the plane, a generalization of Voronoi diagrams based on the maximum distance of a point from a polygon, and show that it is equivalent to the Voronoi diagram of 5 under the Hausdorff distance function. We investigate the structural and combinatorial properties of the Hausdorff Voronoi diagram and give a divide and conquer algorithm for the construction of this diagram that improves upon previous results. As a byproduct we introduce the Hausdorff hull, a structure that relates to the Hausdorff Voronoi diagram in the same way as a convex hull relates to the ordinary Voronoi diagram. The Hausdorff Voronoi diagram finds direct application in the problem of computing the critical area of a VLSI Layout, a measure reflecting the sensitivity of a VLSI design to random manufacturing defects, described in a companion paper. [ABSTRACT FROM AUTHOR]