Results 1  10
of
28
Sorting Selection and Routing on the Array with Reconfigurable Optical Buses
"... In this paper we present efficient algorithms for sorting, selection and packet routing on the AROB (Array with Reconfigurable Optical Buses) model. ..."
Abstract

Cited by 35 (7 self)
 Add to MetaCart
(Show Context)
In this paper we present efficient algorithms for sorting, selection and packet routing on the AROB (Array with Reconfigurable Optical Buses) model.
Mesh Connected Computers with Fixed and Reconfigurable Buses
 Packet Routing, Sorting, and Selection,” Proc. First Annual European Symposium on Algorithms, SpringerVerlag Lecture Notes in Computer Science 726
, 1993
"... Abstract Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of e ..."
Abstract

Cited by 25 (10 self)
 Add to MetaCart
(Show Context)
Abstract Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing and sorting on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k − k routing and k − k sorting on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1 − 1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1 − 1 routing, k − k routing, and k − k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed
A framework for simple sorting algorithms on parallel disk systems
 In Proceedings of the Tenth Annual ACM Symposium on Parallel Algorithms and Architectures
, 1998
"... In this paper we present a simple parallel sorting algorithm and illustrate its application in general sorting, disk sorting, and hypercube sorting. The algorithm (called the (l;m)mergesort (LMM)) is an extension of the bitonic and oddeven mergesorts. Literature on parallel sorting is abundant. Ma ..."
Abstract

Cited by 18 (7 self)
 Add to MetaCart
(Show Context)
In this paper we present a simple parallel sorting algorithm and illustrate its application in general sorting, disk sorting, and hypercube sorting. The algorithm (called the (l;m)mergesort (LMM)) is an extension of the bitonic and oddeven mergesorts. Literature on parallel sorting is abundant. Many of the algorithms proposed, though being theoretically important, may not perform satisfactorily in practice owing to large constants in their time bounds. The algorithm to be presented in this paper has the potential of being practical. We present an application for the parallel disk sorting problem. The algorithm is asymptotically optimal (assuming that N is a polynomial inM, where N is the number of records to be sorted and M is the internal memory size). The underlying constant is very small. This algorithm performs better than the diskstriped mergesort (DSM) algorithm when the number of disks is large. Our implementation is as simple as that of DSM (requiring no fancy data structures or prefetch techniques.) 1 As a second application, we prove that we can get a sparse enumeration sort on the hypercube that is simpler than that of the classical algorithm of Nassimi and Sahni [16]. We also show that Leighton's columnsort algorithm is a special case of LMM. 1
Selection Algorithms for Parallel Disk Systems
, 1998
"... this paper we present deterministic and randomized selection algorithms for parallel disk systems. The algorithms to be presented, in addition to being asymptotically optimal, have small underlying constants in their time bounds and hence have the potential of being practical. ..."
Abstract

Cited by 14 (6 self)
 Add to MetaCart
this paper we present deterministic and randomized selection algorithms for parallel disk systems. The algorithms to be presented, in addition to being asymptotically optimal, have small underlying constants in their time bounds and hence have the potential of being practical.
Permutation routing and sorting on the reconfigurable mesh
 International Journal of Foundations of Computer Science
, 1992
"... Abstract In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
(Show Context)
Abstract In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. Many variations of the reconfigurable mesh can be found in the literature. We define yet another variation which we call as Mr. Wealsomakeuseofthestandard PARBUS model. We showthat permutation routing problem can be solved on a linear array Mr of size n in 3n steps, whereas n − 1 is the best possible run time without recon4 figuration. A trivial lower bound for routing on Mr will be n 2.OnthePARBUS linear array, n is a lower bound and hence any standard nstep routing algorithm will be optimal. We also showthat permutation routing on an n × n reconfigurable mesh Mr can be done in time n + o(n) using a randomized algorithm or in time 1.25n + o(n) deterministically. In contrast, 2n − 2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n−2 steps on a conventional mesh. A lower bound of n 2 is in effect for routing on the 2D mesh Mr as well. On the other 1 hand, n is a lower bound for routing on the PARBUS and our algorithms have the same time bounds on the PARBUS as well. Thus our randomized routing algorithm is optimal upto a lower order term. In addition we show that the problem of sorting can be solved in randomized time n + o(n) onMr as well as on PARBUS. Clearly, this sorting algorithm will be optimal on the PARBUS model. The time bounds of our randomized algorithms hold with high probability.
PDM Sorting Algorithms That Take A Small Number Of Passes, manuscript
, 2004
"... We live in an era of data explosion that necessitates the discovery of novel outofcore techniques. The I/O bottleneck has to be dealt with in developing outofcore methods. The Parallel Disk Model (PDM) has been proposed to alleviate the I/O bottleneck. Sorting is an important problem that has ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We live in an era of data explosion that necessitates the discovery of novel outofcore techniques. The I/O bottleneck has to be dealt with in developing outofcore methods. The Parallel Disk Model (PDM) has been proposed to alleviate the I/O bottleneck. Sorting is an important problem that has ubiquitous applications. Several asymptotically optimal PDM sorting algorithms are known and now the focus has shifted to developing algorithms for problem sizes of practical interest. In this paper we present several novel algorithms for sorting on the PDM that take only a small number of passes through the data. We also present a generalization of the zeroone principle for sorting. A shuffling lemma is presented as well. These lemmas should be of independent interest for average case analysis of sorting algorithms as well as for the analysis of randomized sorting algorithms. 1.
Randomized routing, selection, and sorting on the otismesh
 IEEE Transactions On Parallel And Distributed Systems
, 1998
"... The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. In this paper we present efficient algorithms for packet routing, sorting, and selection on the OTISMesh. The diameter of an ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. In this paper we present efficient algorithms for packet routing, sorting, and selection on the OTISMesh. The diameter of an N 2processor OTISMesh is 4 √ N − 3. We present an algorithm for routing any partial permutation in 4 √ N +o ( √ N) time. Our selection algorithm runs in time 6 √ N + o ( √ N) and our sorting algorithm runs in 8 √ N + o ( √ N) time. All these algorithms are randomized and the stated time bounds hold with high probability. Also, the queue size needed for these algorithms is O(1) with high probability.
A Practical Realization of Parallel Disks
"... Several models of parallel disks are found in the literature. These models have been proposed to alleviate the I/O bottleneck arising in handling voluminous data. These models have the general theme of assuming multiple disks. For instance the Parallel Disk Systems (PDS) model assumes � disks and a ..."
Abstract
 Add to MetaCart
(Show Context)
Several models of parallel disks are found in the literature. These models have been proposed to alleviate the I/O bottleneck arising in handling voluminous data. These models have the general theme of assuming multiple disks. For instance the Parallel Disk Systems (PDS) model assumes � disks and a single computer. It is also assumed that a block of data from each of the � disks can be fetched into the main memory in one parallel I/O operation. In this paper we present a more practical model for multiple disks and evaluate it experimentally. This model is called a Parallel Machine with Disks (PMD). A PMD can be thought of as a realization of the PDS model. A PMD can also be considered as a special case of the hierarchical memory models proposed in the literature. We investigate the sorting problem on the new model. Our analysis demonstrates the practicality of the PMD. We also present experimental confirmation of this aasertion with data from our implementations. 1
Packet Routing and Selection on the POPS Network 1
"... Abstract. Partitioned Optical Passive Stars (POPS) network has been proposed recently as a desirable model of parallel computing. Many papers have been published that address fundamental problems on these networks. Packet routing is one such important problem. We present a randomized algorithm in th ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Partitioned Optical Passive Stars (POPS) network has been proposed recently as a desirable model of parallel computing. Many papers have been published that address fundamental problems on these networks. Packet routing is one such important problem. We present a randomized algorithm in this paper that performs better than the best prior algorithms. We also present a randomized algorithm for selection on the POPS network.
Abstract
"... In this paper we present randomized algorithms for selection and sorting on linear arrays with optical bus communication systems. We show that sorting n given numbers can be performed in O(log n) time with high probability on a linear array, of n processors, with a reconfigurable optical bus system ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper we present randomized algorithms for selection and sorting on linear arrays with optical bus communication systems. We show that sorting n given numbers can be performed in O(log n) time with high probability on a linear array, of n processors, with a reconfigurable optical bus system (LinearAROB). We also show that selection can be performed in O(1) time with high probability on the same parallel machine model. 1