Showing papers by "Michael T. Goodrich published in 1989"

Cascading divide-and-conquer: a technique for designing parallel algorithms

Abstract: Techniques for parallel divide-and-conquer are presented, resulting in improved parallel algorithms for a number of problems. The problems for which improved algorithms are given include segment intersection detection, trapezoidal decomposition, and planar point location. Efficient parallel algorithms are algo given for fractional cascading, three-dimensional maxima, two-set dominance counting, and visibility from a point. All of the algorithms presented run in $O(\log n)$ time with either a linear or a sublinear number of processors in the CREW PRAM model.

Intersecting line segments in parallel with an output-sensitive number of processors

Abstract: An efficient parallel algorithm is given for constructing the arrangement of n line segments in the plane, i.e., the planar graph determined by the segment endpoints and intersections. This algorithm is efficient relative to three efficiency measures--it is an NC algorithm, it has a small time-processor product, and it is output-size sensitive. In particular, it runs in O(logn) time using O(n logn / k) processors, where k is the size of the output (which is (n2) in the worst case). The algorithm does not receive the value of k as input, it determines it on-line. A method for solving an important special case of the segment arrangement problem is also shown, namely, when each input segment is parallel to one of the coordinate axes (i.e., iso-oriented). The algorithm for this problem runs in O(log n) time using an optimal O(n+ k/log n) processors. The model of computation is the CREW PRAM model, where processor allocation must be explicit and global.

Sorting on a parallel pointer machine with applications to set expression evaluation

Abstract: Optimal algorithms for sorting on parallel CREW (concurrent read, exclusive write) and EREW (exclusive read, exclusive write) versions of the pointer machine model are presented. Intuitively, these methods can be viewed as being based on the use of linked lists rather than arrays (the usual parallel data structure). It is shown how to exploit the 'locality' of the approach to solve a problem with applications to database querying and logic programming (set-expression evaluation) in O(log n) time using O(n) processors. >

Sorting on a Parallel Pointer Machine with Applications to Set Expression Evaluation (Preliminary Version)

Abstract: Optimal algorithms for sorting on parallel CREW (concurrent read, exclusive write) and EREW (exclusive read, exclusive write) versions of the pointer machine model are presented. Intuitively, these methods can be viewed as being based on the use of linked lists rather than arrays (the usual parallel data structure). It is shown how to exploit the 'locality' of the approach to solve a problem with applications to database querying and logic programming (set-expression evaluation) in O(log n) time using O(n) processors.<>

Stabbing Parallel Segments with a Convex Polygon (Extended Abstract)

Abstract: We present an algorithm that, given a set of n parallel line segments in the plane, finds a convex polygon whose boundary intersects each segment at least once, or determines that none exists. Our algorithm runs in O(n log n) steps and linear space, which is optimal. Our solution involves a reduction to a bipartite stabbing problem, using a “point-sweeping” or “chain-unwrapping” technique. We use geometric duality to solve bipartite stabbing.

Constructing the Voronoi Diagram of a Set of Line Segments in Parallel (Preliminary Version)

Abstract: In this paper we give a parallel algorithm for constructing the Voronoi diagram of a polygonal scene, i.e., a set of line segments in the plane such that no two segments intersect except possibly at their endpoints. Our algorithm runs in O(log2n) time using O(n) processors in the CREW PRAM model.