We propose a method for constructing a tiling between a pair of planar polygons. Our technique uses multiresolution: tilings of lower resolution polygons are used to construct a tiling for the full resolution polygons. The tilings are constructed using banded refinement, by restricted dynamic programming, in roughly linear time and space. By contrast, the optimal dynamic programming method requires quadratic time and space. In our empirical study of surface reconstruction of brain contours our algorithm exhibited significant speedup over the optimal dynamic program, yet nearly always found an optimal reconstruction. Our approach appears to be generalizable to other geometric problems solvable by dynamic programming, and flexible enough to be tuned for varying data set characteristics. 1 Introduction A typical subproblem of many surface reconstruction algorithms is the fitting of a surface to a set of parallel contours. This problem arises, for example, in medical visualization applic...

We consider the problem of sorting on a one-dimensional subbus array of processors, an architecture that communicates using a segmentable bus. The subbus broadcast operation makes possible a new class of parallel sorting algorithms whose complexity we analyze with the parallel insertion model. We give per-input lower bounds for sorting in the parallel insertion model and demonstrate sorting strategies that are optimal by matching those lower bounds. For each of our sorting strategies, we discuss the issues involved in implementing them on subbus machines. Finally, we empirically evaluate the performance of our sorting strategies by applying them to shearsort, a common two-dimensional mesh sorting algorithm. Our results suggest that for sorting the subbus broadcast capability gives at most a slight advantage over using only nearest neighbor communication.