Efficient plane sweeping in parallel

We present techniques which result in improved parallel algorithms for a number of problems whose efficient sequential algorithms use the plane-sweeping paradigm. The problems for which we give improved algorithms include intersection detection, trapezoidal decomposition, triangulation, and planar point location. Our technique can be used to improve on the previous time bound while keeping the space and processor bounds the same, or improve on the previous space bound while keeping the time and processor bounds the same. We also give efficient parallel algorithms for visibility from a point, 3-dimensional maxima, multiple range-counting, and rectilinear segment intersection counting. We never use the AKS sorting network in any of our algorithms.