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A well-known problem in computational geometry is Klee's measure problem, which asks for the volume of a union of axis-aligned boxes in d-space. In this paper, we consider Klee's measure problem for the special case where a 2-dimensional orthogonal projection of all the boxes has a common corner. We call such a set of boxes <i>2-grounded</i> and, more… (More)

Consider a set of d-dimensional points where the existence or the location of each point is determined by a probability distribution. The convex hull of this set is a random variable distributed over exponentially many choices. We are interested in finding the most likely convex hull, namely, the one with the maximum probability of occurrence. We… (More)

The scheduling needs of umpires and referees differ from the needs of sports teams. In some sports leagues, such as Major League Baseball in the United States, umpires travel throughout the league's territory; they do not have a " home base. " For such leagues, balancing the need to minimize umpire travel and the objective that an umpire should not handle… (More)

Suppose we have a set of n axis-aligned rectangular boxes in d-space, {B1, B2,. .. , Bn}, where each box Bi is active (or present) with an independent probability pi. We wish to compute the expected volume occupied by the union of all the active boxes. Our main result is a data structure for maintaining the expected volume over a dynamic family of such… (More)

We propose an algorithm for the problem of computing shortest paths among curved obstacles in the plane. If the obstacles have O(n) description complexity, then the algorithm runs in O(n log n) time plus a term dependent on the properties of the boundary arcs. Specifically, if the arcs allow a certain kind of <i>bisector intersection</i> to be computed in… (More)

—As a result of the increasing popularity of online social networking sites, millions of people spend a considerable portion of their social life on the Internet. The information exchanged in this context has obvious privacy risks. Interestingly, concerns of social network users about these risks are related not only to adversarial activities but also to… (More)

We consider the problem of computing k shortest paths in a two-dimensional environment with polygonal obstacles , where the jth path, for 1 j k, is the shortest path in the free space that is also homotopically distinct from each of the first j 1 paths. In fact, we consider a more general problem: given a source point s, construct a partition of the… (More)