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View all- Manduhu MJones M(2019)A Work Efficient Parallel Algorithm for Exact Euclidean Distance TransformIEEE Transactions on Image Processing10.1109/TIP.2019.291674128:11(5322-5335)Online publication date: 21-Aug-2019
Work-Time Optimal k-Merge Algorithms on the PRAM
Authors: 
Tatsuya Hayashi, Koji Nakano, and Stephan OlariuAuthors Info & Claims
Tatsuya Hayashi, Koji Nakano, and Stephan OlariuAuthors Info & ClaimsPages 275 - 282
Abstract
For 2 k 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 (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 (log n) time and (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 (log n) time and performs (n log k) work on the EREW-PRAM. Finally, we design a work-time optimal CREW-PRAM k-merge algorithm that runs in (log log n + log k) time and performs (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.
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- Work-Time Optimal k-Merge Algorithms on the PRAM
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Published: 01 March 1998
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View all- Manduhu MJones M(2019)A Work Efficient Parallel Algorithm for Exact Euclidean Distance TransformIEEE Transactions on Image Processing10.1109/TIP.2019.291674128:11(5322-5335)Online publication date: 21-Aug-2019