An optimal parallel algorithm for solving the maximal elements problem in the plane

Abstract We describe an O(log( n )) time with O( n ) processors optimal algorithm for finding the maximal elements of a set. The model of parallel computation we consider is the CREW-PRAM, i.e. it is the synchronous shared memory model where concurrent reads are allowed but no two processors can simultaneously attempt to write in the same memory location (even if they are trying to write the same thing).

[1]  E. Szemerédi,et al.  Sorting inc logn parallel steps , 1983 .

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

[3]  Frank Dehne,et al.  O(n^(1/2)) Algorithms for the Maximal Elements and ECDF Searching Problem on a Mesh-Connected Parallel Computer , 1986, Inf. Process. Lett..

[4]  Mikhail J. Atallah,et al.  Efficient plane sweeping in parallel , 1986, SCG '86.

[5]  János Komlós,et al.  An 0(n log n) sorting network , 1983, STOC.

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

[7]  Frank Thomson Leighton,et al.  Tight Bounds on the Complexity of Parallel Sorting , 1985, IEEE Trans. Computers.

[8]  Larry Rudolph,et al.  The power of parallel prefix , 1985, IEEE Transactions on Computers.