Time- and VLSI-Optimal Convex Hull Computation on Meshes with Multiple Broadcasting

Our main contribution is to present the first known general-case, time- and VLSI-optimal, algorithm for convex hull computation on meshes with multiple broadcasting. Specifically, we show that for every choice of a positive constant e, the convex hull of a set of an arbitrary set of m (n12 + e ⩽ m ⩽ n) points in the plane input in the first ⌉m√n⌈ columns of a mesh with multiple broadcasting of size √n × √n can be computed in Θ (m√n) time.

[1]  Alok Aggarwal.  Optimal Bounds for Finding Maximum on Array of Processors with k Global Buses , 1986, IEEE Transactions on Computers.

[2]  Kang G. Shin,et al.  Implementation of Decentralized Load Sharing in Networked Workstations Using the Condor Package , 1997, J. Parallel Distributed Comput..

[3]  Wen-Tsuen Chen,et al.  Efficient Medain Finding and Its Application to Two-Variable Linear Programming on Mesh-Connected Computers with Multiple Broadcasting , 1992, J. Parallel Distributed Comput..

[4]  Russ Miller,et al.  Efficient Parallel Convex Hull Algorithms , 1988, IEEE Trans. Computers.

[5]  Jerome Rothstein.  Bus automata, brains, and mental models , 1988, IEEE Trans. Syst. Man Cybern..

[6]  Viktor K. Prasanna,et al.  Array Processor with Multiple Broadcasting , 1985, ISCA.

[7]  Stephan Olariu,et al.  A Unifying Look at Semigroup Computations on Meshes with Multiple Broadcasting , 1993, Parallel Process. Lett..

[8]  A. Horn,et al.  Fractal graphics and image compression on a SIMD processor , 1988, Proceedings., 2nd Symposium on the Frontiers of Massively Parallel Computation.

[9]  Oscar H. Ibarra,et al.  Iterative Algorithms for Planar Convex Hull on Mesh-Connected Arrays , 1990, ICPP.

[10]  Sartaj Sahni,et al.  Finding Connected Components and Connected Ones on a Mesh-Connected Parallel Computer , 1980, SIAM J. Comput..

[11]  D. Parkinson,et al.  The AMT DAP 500 , 1988, Digest of Papers. COMPCON Spring 88 Thirty-Third IEEE Computer Society International Conference.

[12]  Leonidas J. Guibas,et al.  Parallel computational geometry , 1988, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[13]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[14]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[15]  Jingyuan Zhang,et al.  Convex Polygon Problems on Meshes with Multiple Broadcasting , 1992, Parallel Process. Lett..

[16]  Jang-Ping Sheu,et al.  Designing Efficient Parallel Algorithms on Mech-Connected Computers with Multiple Broadcasting , 1990, IEEE Trans. Parallel Distributed Syst..

[17]  Bernard Chazelle.  Computational Geometry on a Systolic Chip , 1984, IEEE Transactions on Computers.

[18]  Stephan Olariu,et al.  Optimal convex hull algorithms on enhanced meshes , 1993, BIT Comput. Sci. Sect..

[19]  Amotz Bar-Noy,et al.  Square meshes are not always optimal , 1989, SPAA '89.

[20]  Stephan Olariu,et al.  A Time-Optimal Multiple Search Algorithm on Enhanced Meshes, with Applications , 1994, J. Parallel Distributed Comput..

[21]  Stephan Olariu,et al.  An efficient VLSI architecture for digital geometry , 1994, Proceedings of IEEE International Conference on Application Specific Array Processors (ASSAP'94).

[22]  Hungwen Li,et al.  Connection Autonomy in SIMD Computers: A VLSI Implementation , 1989, J. Parallel Distributed Comput..

[23]  Stephan Olariu,et al.  A Fast Selection Algorithm for Meshes with Multiple Broadcasting , 1994, IEEE Trans. Parallel Distributed Syst..

[24]  Massimo Maresca,et al.  Polymorphic Processor Arrays , 1993, IEEE Trans. Parallel Distributed Syst..

[25]  Peter E. Hart,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[26]  Dionysios I. Reisis,et al.  Image Computations on Meshes with Multiple Broadcast , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Frank Thomson Leighton.  Introduction to parallel algorithms and architectures: arrays , 1992 .

[28]  Russ Miller,et al.  Mesh Computer Algorithms for Computational Geometry , 1989, IEEE Trans. Computers.

[29]  Stephan Olariu,et al.  Square Meshes are not Optimal for Convex Hull Computation , 1993, 1993 International Conference on Parallel Processing - ICPP'93.

[30]  Sartaj Sahni,et al.  Bitonic Sort on a Mesh-Connected Parallel Computer , 1979, IEEE Transactions on Computers.

[31]  Shahid H. Bokhari,et al.  Finding Maximum on an Array Processor with a Global Bus , 1984, IEEE Transactions on Computers.

[32]  Massimo Maresca,et al.  Polymorphic-Torus Network , 1989, IEEE Trans. Computers.

[33]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.