PROVABLY FASTEST PARALLEL ALGORITHMS FOR BIPARTITE PERMUTATION GRAPHS

Provably fastest parallel algorithms for a number of problems on bipartite permutation graphs are presented here. These problems include, among others, connectivity, recognition, isomorphism detection, Hamiltonian path, and shortest path. The algorithms here all run in logarithmic time on CREW PRAM. The processor bound is the same as that for multiplying two matrices in logarithmic time on the model and is subcubic.

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PARALLEL COMPUTATION OF INTERNAL AND EXTERNAL FARTHEST NEIGHBORS IN SIMPLE POLYGONS

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195992000111 ◽

1992 ◽

Vol 02 (02) ◽

pp. 175-190 ◽

Cited By ~ 2

Author(s):

SUMANTA GUHA

Keyword(s):

Parallel Algorithms ◽

Parallel Computation ◽

Shortest Path ◽

Simple Polygon ◽

Divide And Conquer ◽

Simple Polygons ◽

Crew Pram ◽

Serial Algorithm

We present efficient parallel algorithms for two problems in simple polygons: the all-farthest neighbors problem and the external all-farthest neighbors problem. The all-farthest neighbors problem is that of computing, for each vertex p of a simple polygon P, a point ψ(p) in P farthest from p when the distance between p and ψ(p) is measured by the shortest path between them constrained to lie inside P. The external all-farthest neighbors problem is that of computing, for each vertex p of a simple polygon P, a point ϕ(p) on (the boundary of) P farthest from p when the distance between p and ϕ(p) is measured by the shortest path between them constrained to lie outside (the interior of) P. Both our algorithms run in O( log 2 n) time on a CREW PRAM with O(n) processors. Our divide-and-conquer method for the external all-farthest neighbors problem, in fact, leads to a new O(n log n) time serial algorithm that matches the currently best serial algorithm for this problem, but is simpler.

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OPTIMAL PARALLEL ALGORITHMS FOR TRIANGULATED SIMPLE POLYGONS

International Journal of Computational Geometry & Applications ◽

10.1142/s021819599500009x ◽

1995 ◽

Vol 05 (01n02) ◽

pp. 145-170 ◽

Cited By ~ 1

Author(s):

JOHN HERSHBERGER

Keyword(s):

Convex Hull ◽

Parallel Algorithms ◽

Shortest Path ◽

Simple Polygon ◽

Implicit Representation ◽

Shortest Path Tree ◽

Simple Polygons ◽

Pram Model ◽

Crew Pram ◽

Path Queries

We provide optimal parallel solutions to several shortest path and visibility problems set in triangulated simple polygons. Let P be a triangulated simple polygon with n vertices, preprocessed to support shortest path queries. We can find the shortest path tree from any point inside P in O(log n) time using O(n/log n) processors. In the game bounds, we can preprocess P for shooting queries (a query can be answered in O(log n) time by a uniprocessor). Given a set S of m points inside P, we can find an implicit representation of the relative convex hull of S in O(log(nm)) time with O(m) processors. If the relative convex hull has k edges, we can explicitly produce these edges in O(log(nm)) time with O(k/log(nm)) processors. All of these algorithms are deterministic and use the CREW PRAM model.

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