A taxonomy of parallel sorting
ACM Computing Surveys (CSUR)
Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Relational Information Systems
Relational Information Systems
Tight comparison bounds on the complexity of parallel sorting
SIAM Journal on Computing
Optimal parallel merging and sorting without memory conflicts
IEEE Transactions on Computers
An optimally efficient selection algorithm
Information Processing Letters
SIAM Journal on Computing
Journal of Parallel and Distributed Computing
Optimal merging and sorting on the EREW PRAM
Information Processing Letters
Merging multiple lists on hierarchical-memory multiprocessors
Journal of Parallel and Distributed Computing - Special issue on shared-memory multiprocessors
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Fast deterministic approximate and exact parallel sorting
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Parallel computing (2nd ed.): theory and practice
Parallel computing (2nd ed.): theory and practice
Reconstructing a binary tree from its traversals in doubly logarithmic CREW time
Journal of Parallel and Distributed Computing
IEEE Transactions on Parallel and Distributed Systems
Journal of Parallel and Distributed Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Parallel computation: models and methods
Parallel computation: models and methods
Join and Semijoin Algorithms for a Multiprocessor Database Machine
ACM Transactions on Database Systems (TODS)
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Data Structures and Algorithms
Data Structures and Algorithms
Parallel Algorithms for Partitioning Sorted Sets and Related Problems
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
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For 2 驴k驴n, the k-merge problem is to merge a collection of k sorted sequences of total length n into a new sorted sequence. The k-merge problem is fundamental as it provides a common generalization of both merging and sorting. The main contribution of this work is to give simple and intuitive work-time optimal algorithms for the k-merge problem on three PRAM models, thus settling the status of the k-merge problem. We first prove that 驴(n log k) work is required to solve the k-merge problem on the PRAM models. We then show that the EREW-PRAM and both the CREW-PRAM and the CRCW require 驴(log n) time and 驴(log log n + log k) time, respectively, provided that the amount of work is bounded by O(n log k). Our first k-merge algorithm runs in 驴(log n) time and performs 驴(n log k) work on the EREW-PRAM. Finally, we design a work-time optimal CREW-PRAM k-merge algorithm that runs in 驴(log log n + log k) time and performs 驴(n log k) work. This latter algorithm is also work-time optimal on the CRCW-PRAM model. Our algorithms completely settle the status of the k-merge problem on the three main PRAM models.