1 The farthest-point Voronoi diagram of a set of n sites 2 is a tree with n leaves. We investigate whether arbi3 trary trees can be realized as farthest-point Voronoi di4 agrams. Given an abstract ordered tree T with n leaves 5 and prescribed edge lengths, we produce a set of n sites 6 S in O(n) time such that the farthest-point Voronoi di7 agram of S represents T . We generalize this algorithm...

We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest neighbors, we show how to find (1+ ε)-approximate farthest neighbors in time O(logn) per query in D-dimensional Euclidean space for any constants D and ε. A...

Let be a set of points in convex position in . The farthest-point Voronoi diagram of partitions into convex cells. We consider the intersection of the diagram with the boundary of the convex hull of . We give an algorithm that computes an implicit representation of in expected time. More precisely, we compute the combinatorial structure of , the coordinates of its vertices, and the equation of ...

We present a new 12CO(J=1–0)–line survey of the Andromeda galaxy, M 31, with the highest resolution to date (23, or 85 pc along the major axis), observed On-the-Fly with the IRAM 30-m telescope. We mapped an area of about 2 ×0. 5 which was tightly sampled on a grid of 9 with a velocity resolution of 2.6 km s−1. The r.m.s. noise in the velocity-integrated map is around 0.35 K km s−1 on the Tmb-s...

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network distance. Within this metric space, we study farthest points. We introduce network farthest-point diagrams, which capture how the farthest points—and the distan...

Statewide land cover change detection analysis provides a useful tool for conservation planning and environmental monitoring and addresses issues of habitat fragmentation and urban sprawl. Furthermore, using historical and recent land cover data offers two perspectives on landscape dynamics. To this end, the first alliance level land cover map of Kansas recently completed by the KARS Program wa...

Given a set of sites (points) in a simple polygon, the farthest-point geodesic Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an O((n + m) log logn)time algorithm to compute the farthest-point geodesic Voronoi diagram for m sites lying on the boundary of a si...

[1] Six years of daily satellite data are used to quantify and map intraseasonal variability of chlorophyll and sea surface temperature (SST) in the California Current. We define intraseasonal variability as temporal variation remaining after removal of interannual variability and stationary seasonal cycles. Semivariograms are used to quantify the temporal structure of residual time series. Emp...