Let P be a convex polygon with n vertices. We want to find two congruent disks whose union covers P and whose radius is minimized. We also consider its discrete version with centers restricted to beâ€¦ (More)

Let P be a set of n points in the plane. The geometric minimum-diameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that thereâ€¦ (More)

Let P and Q be disjoint polygons in the plane. We consider the problem of finding an optimal bridge (p,q) , pâˆˆ \partial P and qâˆˆ \partial Q , such that the length of the longest path from a point inâ€¦ (More)

Let P be a simple polygon. We define a witness set W to be a set of points such that if any (prospective) guard set G guards W , then it is guaranteed that G guards P . We show that not all polygonsâ€¦ (More)

In this paper we discuss farthest-point problems, in which a sequence S = (p1, p2, . . . , pn) of n points in the plane is given in advance and can be preprocessed to answer various queriesâ€¦ (More)

Annotating maps, graphs, and diagrams with pieces of text is an important step in information visualization that is usually referred to as label placement. We define nine label-placement models forâ€¦ (More)

Let S be a set of n points in the plane. We present data structures that solve range-aggregate query problems on three geometric extent measure problems. Using these data structures, we can report,â€¦ (More)