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### On parallel integer sorting

Sanguthevar Rajasekaran, Sandeep Sen
1992 Acta Informatica
Known Parallel Sorting Algorithms The performance of a parallel algorithm can be specified by bounds on its principal resources namely, processors and time.  ...  Using this algorithm, the best known upper bound for integer sorting on the (O(log n) word length) EREW PRAM model is improved.  ...  But no parallel analogue of this algorithm exists. In this section we present a parallel range reduction algorithm that results in a P T bound of O(n √ log n) for INTEGER SORT on the CRCW PRAM.  ...

### A NOTE ON COARSE GRAINED PARALLEL INTEGER SORTING

A. CHAN, F. DEHNE
1999 Parallel Processing Letters
We observe that for n=p p, which is usually the case in practice, there exists a very simple, deterministic, optimal coarse grained parallel integer sorting algorithm with 24 communication rounds (6 n  ...  p -relations and 18 p-relations), On=p memory per processor and On=p local computation.  ...  Algorithms 2: Sorting n integers on a p processors machine when n p p.  ...

### An optimal parallel algorithm for integer sorting

John H. Reif
1985 26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
Our main result is an optimal randomized parallel algorithm for INTE-GER SORT i.e., for sorting n integers in the range 1; n .  ...  And nally, w e present sub-logarithmic time algorithms for GENERAL SORT and INTEGER SORT. Our sublogarithmic GENERAL SORT algorithm is also optimal.  ...  step2 1 an optimal parallel algorithm for INTEGER SORT.  ...

### A Note on Coarse Grained Parallel Integer Sorting [chapter]

A. Chan, F. Dehne
High Performance Computing Systems and Applications
We observe that for n=p p, which is usually the case in practice, there exists a very simple, deterministic, optimal coarse grained parallel integer sorting algorithm with 24 communication rounds (6 n  ...  p -relations and 18 p-relations), On=p memory per processor and On=p local computation.  ...  Algorithms 2: Sorting n integers on a p processors machine when n p p.  ...

### Integer sorting algorithms for coarse-grained parallel machines

K. Alsabti, S. Ranka
Proceedings Fourth International Conference on High-Performance Computing
These results are compared with two other well known practical parallel sorting algorithms based on radix sort and sample sort.  ...  Integer sorting is a subclass of the sorting problem where the elements have integer values and the largest element is polynomially bounded in the number of elements to be sorted.  ...  the performance of our algorithm is comparable or superior to the sample based integer sort for small sized integers (16-bit or 32-bit) especially for large data sets or number of processors.  ...

### Integer sorting on a mesh-connected array of processors

D. Krizanc
Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing 1990
Using a less restrictive, more realistic model we show that the sorting N = n 2 integers in the range [1 ... N] can be performed in 2n + o(n) steps on a n X n mesh.  ...  Schnorr and Shamir and independently Kunde, have shown that sorting N = n 2 inputs into snake-like ordering on a n X n mesh requires 3n -o(n) steps.  ...  Theorem 3 N = n 2 integers in the range [1 ... N] can be sorted into snake like order in 2n + o(n) steps on a n X n mesh. Proof: A sorted list of k integers in the range [1 ...  ...

### Sorting using networks of deques

A. Nozaki
1979 Journal of computer and system sciences (Print)
The number of required deques for sorting all sequences of n items in a parallel or series network of deques is considered.  ...  For sorting all sequences of n integers by a series networks of stacks, we need O(log n) stacks.  ...  For the case when n is equal to one, the theorem is trivially true: No IRDQ is required for sorting one integer. So we prove the theorem by induction on n.  ...

### Parallel Merging and Sorting on Linked List

Yijie Han, Sreevalli Tata
2021 International Journal of Computer and Information Technology(2279-0764)
We also show that two sorted linked lists of n integers in {0, 1, ..., m} can be merged into one sorted linked list in O(log(c)n(loglogm)1/2) time using n/(log(c)n(loglogm)1/2) processors, where c is an  ...  We study linked list sorting and merging on the PRAM model.  ...  INTRODUCTION In this paper we study parallel merging and sorting.  ...

### More Efficient Parallel Integer Sorting [chapter]

Yijie Han, Xin He
2012 Lecture Notes in Computer Science
We present a more efficient CREW PRAM algorithm for integer sorting.  ...  This algorithm sorts n integers in {0, 1, 2, ..., n 1/2 } in O((log n) 3/2 / log log n) time and O(n(log n/ log log n) 1/2 ) operations.  ...  Parallel integer sorting is such a fundamental problem in parallel algorithm design and many renowned researchers worked on this problem relentlessly.  ...

### A Parallel Solution to Finding Nodal Neighbors in Generic Meshes [article]

Gang Mei, Nengxiong Xu, Hong Tian, Shengwei Li
2016 arXiv   pre-print
The presented parallel solution is heavily dependent on the parallel sorting, scan, and reduction, and can be applied to determine both the neighboring nodes and elements.  ...  In this paper we specifically present a parallel solution to finding the one-ring neighboring nodes and elements for each vertex in generic meshes.  ...  Our solution is a topology-based method, and is heavily dependent on the use of parallel sorting, scan, and reduction.  ...

### A Parallel Solution to Finding Nodal Neighbors in Generic Meshes

Pian Qi, Gang Mei, Nengxiong Xu, Hong Tian
2020 MethodsX
The presented parallel solution is heavily dependent on the parallel sorting, scan, and reduction.  ...  In this paper we specifically present a parallel solution to finding the one-ring neighboring nodes and elements for each vertex in generic meshes.  ...  The presented parallel solution is heavily dependent on the parallel sorting, scan, and reduction.  ...

### An NC Algorithm for Sorting Real Numbers in O(nlogn/√loglogn) Operations

Yijie Han, Sneha Mishra, Md Usman Gani Syed
2019 Open Journal of Applied Sciences
We apply the recent important result of serial sorting of n real numbers in ( ) log O n n time to the design of a parallel algorithm for sorting real numbers in ( ) 1 log O n ε + time and log log log operations  ...  This is the first NC algorithm known to take ( ) log o n n operations for sorting real numbers.  ...  There are also parallel algorithms for integer sorting    . In the case of integer sorting, the operation bound can be improved to below ( ) log O n n .  ...

### AA-Sort: A New Parallel Sorting Algorithm for Multi-Core SIMD Processors

Hiroshi Inoue, Takao Moriyama, Hideaki Komatsu, Toshio Nakatani
2007 Parallel Architecture and Compilation Techniques (PACT), Proceedings of the International Conference on
970MP when sorting 32 M of random 32-bit integers.  ...  Furthermore, a parallel version of AA-sort demonstrated better scalability with increasing numbers of cores than a parallel version of GPUTeraSort on both platforms. 16th International Conference on Parallel  ...  Figure 12 shows the execution time of parallel versions of the AA-sort and the GPUTeraSort on 1, 2, and 4 PowerPC 970MP cores for 32 M random integers.  ...