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Deterministic Sorting in Nearly Logarithmic Time on the Hypercube and Related Computers
 Journal of Computer and System Sciences
, 1996
"... This paper presents a deterministic sorting algorithm, called Sharesort, that sorts n records on an nprocessor hypercube, shuffleexchange, or cubeconnected cycles in O(log n (log log n) 2 ) time in the worst case. The algorithm requires only a constant amount of storage at each processor. Th ..."
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Cited by 67 (10 self)
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This paper presents a deterministic sorting algorithm, called Sharesort, that sorts n records on an nprocessor hypercube, shuffleexchange, or cubeconnected cycles in O(log n (log log n) 2 ) time in the worst case. The algorithm requires only a constant amount of storage at each processor. The fastest previous deterministic algorithm for this problem was Batcher's bitonic sort, which runs in O(log 2 n) time. Supported by an NSERC postdoctoral fellowship, and DARPA contracts N0001487K825 and N00014 89J1988. 1 Introduction Given n records distributed uniformly over the n processors of some fixed interconnection network, the sorting problem is to route the record with the ith largest associated key to processor i, 0 i ! n. One of the earliest parallel sorting algorithms is Batcher's bitonic sort [3], which runs in O(log 2 n) time on the hypercube [10], shuffleexchange [17], and cubeconnected cycles [14]. More recently, Leighton [9] exhibited a boundeddegree,...
Fast Algorithms for BitSerial Routing on a Hypercube
, 1991
"... In this paper, we describe an O(log N)bitstep randomized algorithm for bitserial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of online circuit switching in ..."
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Cited by 36 (9 self)
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In this paper, we describe an O(log N)bitstep randomized algorithm for bitserial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of online circuit switching in an O(1)dilated hypercube (i.e., the problem of establishing edgedisjoint paths between the nodes of the dilated hypercube for any onetoone mapping). Our algorithm is adaptive and we show that this is necessary to achieve the logarithmic speedup. We generalize the BorodinHopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithmic degree network requires at least \Omega\Gammaast 2 N= log log N) bit steps with high probability for almost all permutations. 1 Introduction Substantial effort has been devoted to the study of storeandforward packet routing algorithms for hypercubic networks. The fastest algorithms are randomized, and c...
Reconfiguration With Time Division Multiplexed MINs for Multiprocessor Communications
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... In this paper, timedivision multiplexed multistage interconnection networks (TDMMINs) are proposed for multiprocessor communications. Connections required by an application are partitioned into a number of subsets called mappings, such that connections in each mapping can be established in a MI ..."
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Cited by 35 (29 self)
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In this paper, timedivision multiplexed multistage interconnection networks (TDMMINs) are proposed for multiprocessor communications. Connections required by an application are partitioned into a number of subsets called mappings, such that connections in each mapping can be established in a MIN without conflict. Switch settings for establishing connections in each mapping are determined and stored in shift registers. By repeatedly changing switch settings, connections in each mapping are established for a time slot in a roundrobin fashion. Thus, all connections required by an application may be established in a MIN in a timedivision multiplexed way. TDMMINs can emulate a completely connected network using N time slots. It can also emulate regular networks such as rings, meshes, CubeConnectedCycles (CCC), binary trees and n dimensional hypercubes using 2, 4, 3, 4 and n time slots, respectively. The problem of partitioning an arbitrary set of requests into a minimal ...
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.
Randomized Protocols for LowCongestion Circuit Routing in Multistage Interconnection Networks
"... In this paper we study randomized algorithms for circuit switching on multistage networks related to the butterfly. We devise algorithms that route messages by constructing circuits (or paths) for the messages with small congestion, dilation, and setup time. Our algorithms are based on the idea of h ..."
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Cited by 14 (5 self)
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In this paper we study randomized algorithms for circuit switching on multistage networks related to the butterfly. We devise algorithms that route messages by constructing circuits (or paths) for the messages with small congestion, dilation, and setup time. Our algorithms are based on the idea of having each message choose a route from two possibilities, a technique that has previously proven successful in simpler load balancing settings. As an application of our techniques, we propose a novel design for a data server.
Implementation Of Neural Networks On Parallel Architectures
, 1992
"... xi 1 Introduction 1 1.1 Problem Statement : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2 The Neuron : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.2.1 Biological Model : : : : : : : : : : : : : : : : : : : : : : 7 1.2.2 Computational Model : : : : : : : : : : : : : : : : : : ..."
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Cited by 9 (6 self)
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xi 1 Introduction 1 1.1 Problem Statement : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2 The Neuron : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.2.1 Biological Model : : : : : : : : : : : : : : : : : : : : : : 7 1.2.2 Computational Model : : : : : : : : : : : : : : : : : : : 9 1.3 Implementation Technologies : : : : : : : : : : : : : : : : : : : : 11 1.4 State of the Art : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 1.5 Summary of Results : : : : : : : : : : : : : : : : : : : : : : : : 16 2 Implementation of Neural Models with Static Links 19 2.1 ANN Models with Static Links : : : : : : : : : : : : : : : : : : 20 2.1.1 The Hopfield Model : : : : : : : : : : : : : : : : : : : : : 21 2.1.2 The Perceptron Model : : : : : : : : : : : : : : : : : : : 23 2.1.3 The MultiLayer Model : : : : : : : : : : : : : : : : : : : 24 2.2 Basic Computational Requirements : : : : : : : : : : : : : : : : 25 2.2.1 Search Phase Computations : : : : : : : : : : : : : : ...
Interconnection networks using shuffles
 IEEE Computers
, 1981
"... techniques allow severalprocessors within a multiprocessing ..."
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Cited by 9 (0 self)
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techniques allow severalprocessors within a multiprocessing
Parallel Routing Algorithms for Nonblocking Electronic and Photonic Switching Networks
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2005
"... We study the connection capacity of a class of rearrangeable nonblocking (RNB) and strictly nonblocking (SNB) networks with/without crosstalkfree constraint, model their routing problems as weak or strong edgecolorings of bipartite graphs, and propose efficient routing algorithms for these network ..."
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Cited by 8 (3 self)
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We study the connection capacity of a class of rearrangeable nonblocking (RNB) and strictly nonblocking (SNB) networks with/without crosstalkfree constraint, model their routing problems as weak or strong edgecolorings of bipartite graphs, and propose efficient routing algorithms for these networks using parallel processing techniques. This class of networks includes networks constructed from Banyan networks by horizontal concatenation of extra stages and/or vertical stacking of multiple planes. We present a parallel algorithm that runs in Oðlg 2 NÞ time for the RNB networks of complexities ranging from OðN lg NÞ to OðN1:5 pffiffiffiffi lg NÞ crosspoints 1:5 and parallel algorithms that run in Oðminfd lg N; NgÞ time for the SNB networks of OðN lg NÞ crosspoints, using a completely connected multiprocessor system of N processing elements. Our algorithms can be translated into algorithms with an Oðlg N lg lg NÞ slowdown factor for the class of Nprocessor hypercubic networks, whose structures are no more complex than a single plane in the RNB and SNB networks considered.
A study of permutation networks: some generalizations and tradeoffs
 Jour. of
, 1994
"... Permutation switching is a critical element of many computer and communication systems. Within a group theoretical framework, this paper provides an indepth study of permutation networks, and examines the tradeoffs between network cost and set up or routing time. It introduces the notion of an (n, r ..."
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Cited by 4 (0 self)
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Permutation switching is a critical element of many computer and communication systems. Within a group theoretical framework, this paper provides an indepth study of permutation networks, and examines the tradeoffs between network cost and set up or routing time. It introduces the notion of an (n, r, q)permuter, i.e., a permuter with n inputs and r outputs that can realize all q! permutations between any q of its n inputs and q of its r outputs, where q ≤ r ≤ n. This generalization accounts for a switching environment where the maximum number of simultaneous paths may be less than the actual number of inputs and outputs. It is shown that the previously known designs, such as Clos networks result in inferior realizations of (n, r, q)permuters. Using concentrators, the paper gives new network designs that lead to (n, r, q)permuters with asymptotically minimum cost and quadlogarithmic routing time for all q ≤ r. More specifically, for q = O(lg n) and q = O(n ɛ), where 0 <ɛ<1, an (n, r, q)permuter with O(n) switches is given 1. For the same values of q, Clos designs require at least n lg lg n and n lg n switches. Another advantage of the new designs is that they do not require complex routing schemes as Clos networks since they are inherently selfrouting. It is also established that, when q = n = r, these same designs can be extended to permuters with O(n lg n) switches.