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15
Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 29 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.
Derivation of Randomized Sorting and Selection Algorithms, in Parallel Algorithm Derivation And Program Transformation, edited by
, 1993
"... In this paper we systematically derive randomized algorithms (both sequential and parallel) for sorting and selection from basic principles and fundamental techniques like random sampling. We prove several sampling lemmas which will find independent applications. The new algorithms derived here are ..."
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Cited by 22 (18 self)
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In this paper we systematically derive randomized algorithms (both sequential and parallel) for sorting and selection from basic principles and fundamental techniques like random sampling. We prove several sampling lemmas which will find independent applications. The new algorithms derived here are the most efficient known. From among other results, we have an efficient algorithm for sequential sorting. The problem of sorting has attracted so much attention because of its vital importance. Sorting with as few comparisons as possible while keeping the storage size minimum is a long standing open problem. This problem is referred to as ‘the minimum storage sorting ’ [10] in the literature. The previously best known minimum storage sorting algorithm is due to Frazer and McKellar [10]. The expected number of comparisons made by this algorithm is n log n + O(n log log n). The algorithm we derive in this paper makes only an expected n log n + O(n ω(n)) number of comparisons, for any function ω(n) that tends to infinity. A variant of this algorithm makes no more than n log n + O(n log log n) comparisons on any input of size n with overwhelming probability. We also prove high probability bounds for several randomized algorithms for which only expected bounds have been proven so far.
Sorting and Selection on Interconnection Networks
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1995
"... ABSTRACT. In this paper we identify techniques that havebeen employed in the design of sorting and selection algorithms for various interconnection networks. We consider both randomized and deterministic techniques. Interconnection Networks of interest include the mesh, the mesh with xed and recon g ..."
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Cited by 21 (15 self)
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ABSTRACT. In this paper we identify techniques that havebeen employed in the design of sorting and selection algorithms for various interconnection networks. We consider both randomized and deterministic techniques. Interconnection Networks of interest include the mesh, the mesh with xed and recon gurable buses, the hypercube family, and the star graph. For the sake of comparisons, we also list PRAM algorithms. 1
Routing and Sorting on Meshes with Row and Column Buses
, 1994
"... of the 27th Annual IEEE Symposium on Foundations of Computer Science, pages 264273, 1986. [50] T. Suel. Routing and sorting on meshes with row and column buses. In Proceedings of the 8th International Parallel Processing Symposium, April 1994. [51] B. Wang and G. Chen. Constant time algorithms fo ..."
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Cited by 13 (1 self)
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of the 27th Annual IEEE Symposium on Foundations of Computer Science, pages 264273, 1986. [50] T. Suel. Routing and sorting on meshes with row and column buses. In Proceedings of the 8th International Parallel Processing Symposium, April 1994. [51] B. Wang and G. Chen. Constant time algorithms for the transitive closure and some related graph problems on processor arrays with reconfigurable bus systems. IEEE Transactions on Parallel and Distributed Systems, 1:500507, 1990. [27] M. Kunde. Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound. In Proceedings of the 1st Annual European Symposium on Algorithms, September 1993. [28] R. E. Ladner, J. Lampe, and R. Rogers. Vector prefix addition on subbus mesh computers. In Proceedings of the 5th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 387396, June 1993. [29] F. T. Leighton. Tight bounds on the com
Selection, Routing, and Sorting on the Star Graph
 Proceedings of the International Parallel Processing Symposium
, 1993
"... We consider the problems of selection, routing and sorting on an nstar graph (with n! nodes),an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a ‘(k, 1,k) chain network’) of the star graph which enables us to desi ..."
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Cited by 10 (3 self)
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We consider the problems of selection, routing and sorting on an nstar graph (with n! nodes),an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a ‘(k, 1,k) chain network’) of the star graph which enables us to design efficient algorithms for the above mentioned problems. We present an algorithm that performs a sequence of n prefix computations in O(n 2) time. This algorithm is used as a subroutine in our other algorithms. We also show that sorting can be performed on the nstar graph in time O(n 3) and that selection of a set of uniformly distributed n keys can be performed in O(n 2) time with high probability. Finally, we also present a deterministic (non oblivious) routing algorithm that realizes any permutation in O(n 3) steps on the nstar graph. There exists an algorithm in the literature that can perform a single prefix computation in O(n lg n) time. The best known previous algorithm for sorting has a run time of O(n 3 lg n) and is deterministic. To our knowledge, the problem of selection has not been considered before on the star graph. 1
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. ..."
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Cited by 9 (3 self)
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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.
Overview of Mesh Results
 MAXPLANCK INSTITUT FUR INFORMATIK, SAARBRUCKEN
, 1995
"... This paper provides an overview of lower and upper bounds for algorithms for meshconnected processor networks. Most of our attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and ..."
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Cited by 8 (0 self)
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This paper provides an overview of lower and upper bounds for algorithms for meshconnected processor networks. Most of our attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a workedout version of the author's contribution to a joint paper with Miltos D. Grammatikakis, D. Frank Hsu and Miro Kraetzl on multicomputer routing, submitted to the Journal of Parallel and Distributed Computing.
Efficient Self Simulation Algorithms for Reconfigurable Arrays
, 1995
"... There are several reconfiguringnetwork models of parallel computation that are considered in the published literature, depending on their switching capabilities. Can these reconfigurable models be the basis for the design of massively parallel computers? Perhaps the most fundamental related issue i ..."
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Cited by 7 (1 self)
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There are several reconfiguringnetwork models of parallel computation that are considered in the published literature, depending on their switching capabilities. Can these reconfigurable models be the basis for the design of massively parallel computers? Perhaps the most fundamental related issue is virtual parallelism, or the self simulation problem: given an algorithm which is designed for a large reconfigurable mesh, can it be executed efficiently on a smaller reconfigurable mesh? In this work we give several positive answers to the self simulation problem. We show that the simulation of a reconfiguring mesh by a smaller one can be carried optimally and using standard methods on the model in which buses are established along rows or along columns. A novel technique is shown to achieve asymptotically optimal self simulation on models which allow buses to switch column and row edges, provided that a bus is a "linear" path of connected edges. Finally, for models in which a bus is any ...
Sorting by Parallel Insertion on a OneDimensional SubBus Array
 IEEE Trans. on Computers
, 1996
"... We consider the problem of sorting on a onedimensional subbus array of processors. The subbus broadcast operation makes possible a new class of parallel sorting algorithms whose complexity we analyze with the parallel insertion model. A sorting method, or sorting strategy, in the parallel insert ..."
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Cited by 1 (0 self)
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We consider the problem of sorting on a onedimensional subbus array of processors. The subbus broadcast operation makes possible a new class of parallel sorting algorithms whose complexity we analyze with the parallel insertion model. A sorting method, or sorting strategy, in the parallel insertion model, uses a sequence of left and right insertion steps, of which we give two types: greedy insertion steps and simple insertion steps. For two restricted classes of parallel insertion sorting, the oneway and the alternating sorting strategies, we give lower bounds and optimal sorting strategies that exactly match the lower bounds. Optimal alternating sorting strategies are demonstrated to use a factor of two fewer insertion steps on average than oddeven transposition sort and any optimal oneway sorting strategy. For general sorting strategies, we give a weak lower bound and consider a sorting strategy that uses the fewest greedy insertion steps. Finally, we discuss the issues involve...