On Parallel Integer Merging

The problem of merging two sorted arrays A = (a1, a2, ..., an1) and B = (b1, b2, ..., bn2) is considered. For input elements that are drawn from a domain of integers 1...s] we present an algorithm that runs in O(log log log s) time using n/log log log s CREW PRAM processors (optimal speed-up) and O(ns?) space, where n = n1 + n2. For input elements that are drawn from a domain of integers 1...n] we present a second algorithm that runs in O(?(n)) time (where ?(n) is the inverse of Ackermann?s function) using n/?(n) CREW PRAM processors and linear space. This second algorithm is non-uniform; however, it can be made uniform at a price of a certain loss of speed, or by using a CRCW PRAM.

[1]  Stephen A. Cook,et al.  Upper and Lower Time Bounds for Parallel Random Access Machines without Simultaneous Writes , 1986, SIAM J. Comput..

[2]  Friedhelm Meyer auf der Heide,et al.  The complexity of parallel sorting , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[3]  Larry Rudolph,et al.  Counting and Packing in Parallel , 1986, ICPP.

[4]  Uzi Vishkin,et al.  Finding all nearest neighbors for convex polygons in parallel: A new lower bound technique and a matching algorithm , 1990, Discret. Appl. Math..

[5]  Uzi Vishkin,et al.  Recursive Star-Tree Parallel Data Structure , 1993, SIAM J. Comput..

[6]  Robert E. Tarjan,et al.  Efficiency of a Good But Not Linear Set Union Algorithm , 1972, JACM.

[7]  Micha Sharir,et al.  Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes , 1986, FOCS.

[8]  Uzi Vishkin,et al.  On Parallel Hashing and Integer Sorting , 1991, J. Algorithms.

[9]  Torben Hagerup,et al.  Towards Optimal Parallel Bucket Sorting , 1987, Inf. Comput..

[10]  Sanguthevar Rajasekaran,et al.  Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms , 1989, SIAM J. Comput..

[11]  Richard Cole,et al.  Deterministic Coin Tossing with Applications to Optimal Parallel List Ranking , 2018, Inf. Control..

[12]  Leslie G. Valiant,et al.  Parallelism in Comparison Problems , 1975, SIAM J. Comput..

[13]  Clyde P. Kruskal,et al.  Searching, Merging, and Sorting in Parallel Computation , 1983, IEEE Transactions on Computers.

[14]  Krzysztof Diks,et al.  Improved Deterministic Parallel Integer Sorting , 1991, Inf. Comput..

[15]  Allen Van Gelder.  PRAM Processor Allocation: A Hidden Bottleneck in Sublogarithmic Algorithms , 1989, IEEE Trans. Computers.

[16]  Allan Borodin,et al.  Routing, Merging, and Sorting on Parallel Models of Computation , 1985, J. Comput. Syst. Sci..

[17]  Uzi Vishkin,et al.  Finding the maximum, merging and sorting in a parallel computation model , 1981, CONPAR.