Leftmost one Computation on Meshes with Row Broadcasting

Abstract Given a matrix of size √ n ×√ n with every entry being a 0 or a 1, the leftmost-one problem asks to determine the position of the leftmost 1, if any, in each row of the matrix. The leftmost-one problem finds applications in image processing, digitized geometry and computer graphics, among others. Recently, an O( n 1 6 ) time solution to the leftmost-one problem on a mesh with row buses has been proposed. However, the computational model assumes that processors have unbounded memory. We show that the problem can be solved in O( n 1 6 ) time on a √ n ×√ n mesh with row broadcasting, even if each processor has only a constant number of registers.

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

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

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

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

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

[6]  Quentin F. Stout,et al.  Mesh-Connected Computers with Broadcasting , 1983, IEEE Transactions on Computers.

[7]  Quentin F. Stout,et al.  Meshes with multiple buses , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

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

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

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

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