On Parallel Integer Merging

Simplified, stable parallel merging

This note makes an observation that significantly simplifies previous parallel, two-way merge algorithms based on binary search and sequential merge in parallel. First, it is shown that the additional merge step of distinguished elements as found in previous algorithms is not necessary , thus simplifying the implementation and reducing constant factors. Second, by fixating the requirements to t...

Large Integer Multiplication on Massively Parallel Processors

We present results of a technique for multiplying large integers using the Fermat Number Transform. When the Fermat Number Transform was first proposed, word length constraints limited its effectiveness. Despite the development of multidimensional techniques to extend the length of the FNT, the relatively small word length of existing machines made the transform of little more than academic int...

Integer preemptive scheduling on parallel machines

We consider preemptive machine scheduling problems on identical parallel machines. It is shown that every such problem with chain-like precedence constraints, release dates and a regular unit-concave objective function has the following integer preemption property : for any problem instance with integral input data there exists an optimal schedule where all interruptions (as well as starting an...

On Parallel Hashing and Integer Sorting

On Parallel Hashing and Integer Sorting

The problem of sorting n integers from a restricted range [1..m], where m is superpolynomial in n, is considered. An o(nlog n) randomized algorithm is given. Our algorithm takes O(n log log m) expected time and 0(n) space. (Thus, for m nv ) we have an 0(n log log n) algorithm.) The algorithm is parallelizable. The resulting parallel algorithm achieves optimal speed up. Some features of the algo...