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16
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 35 (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.
Practical Parallel Algorithms for Personalized Communication and Integer Sorting
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMICS
, 1995
"... A fundamental challenge for parallel computing is to obtain highlevel, architecture independent, algorithms which efficiently execute on generalpurpose parallel machines. With the emergence of message passing standards such as MPI, it has become easier to design efficient and portable parallel alg ..."
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Cited by 28 (5 self)
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A fundamental challenge for parallel computing is to obtain highlevel, architecture independent, algorithms which efficiently execute on generalpurpose parallel machines. With the emergence of message passing standards such as MPI, it has become easier to design efficient and portable parallel algorithms by making use of these communication primitives. While existing primitives allow an assortment of collective communication routines, they do not handle an important communication event when most or all processors have nonuniformly sized personalized messages to exchange with each other. We focus in this paper on the hrelation personalized communication whose efficient implementation will allow high performance implementations of a large class of algorithms. While most previous hrelation algorithms use randomization, this paper presents a new deterministic approach for hrelation personalized communication with asymptoticaly optimal complexity for h p². As an application, we ...
Routing on Meshes with Buses
"... We consider the problem of routing packets on an n \Theta \Delta \Delta \Delta \Theta n MIMD meshconnected array of processors augmented with row and column buses. We give lower bounds and randomized algorithms for the problem of routing kpermutations (where each processor is the source and desti ..."
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Cited by 9 (3 self)
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We consider the problem of routing packets on an n \Theta \Delta \Delta \Delta \Theta n MIMD meshconnected array of processors augmented with row and column buses. We give lower bounds and randomized algorithms for the problem of routing kpermutations (where each processor is the source and destination of exactly k packets) on a ddimensional mesh with buses, which we call the (k; d)routing problem. We give a general class of "hard" permutations which we use to prove lower bounds for the (k; d)routing problem, for all k; d 1. For the (1; 1) and (1; 2)routing problems the worstcase permutations from this class are identical to ones published by other authors, as are the resulting lower bounds. However, we further show that the (1; d) routing problem requires 0:72 \Delta n steps for d = 3, 0:76 \Delta n steps for d = 4 and slightly more than (1 \Gamma 1=d) \Delta n steps for all d 5. We also obtain new lower bounds for the (k; d)routing problem for k; d ? 1, which improve on t...
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.
Simulating PRAM with a MSIMD Model (ASC)
 In Proc. International Conference on Parallel Processing
, 1998
"... The ASC (MSIMD) model for parallel computation supports a generalized version of an associative style of computing that has been used since the introduction of associative SIMD computers in the early 1970's. In particular, this model supports data parallelism, constant time maximum and minimum ..."
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Cited by 4 (2 self)
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The ASC (MSIMD) model for parallel computation supports a generalized version of an associative style of computing that has been used since the introduction of associative SIMD computers in the early 1970's. In particular, this model supports data parallelism, constant time maximum and minimum operations, one or more instruction streams (ISs) which are sent to an equal number of partition sets of processors, assignment of tasks to the ISs using control parallelism. ASC also allows a network to interconnect the processing elements (PEs). This paper shows how ASC can be simulated with synchronous PRAM, and the converse. These results provide an important step in de ning the power of associative model in terms of PRAM which is the most well studied parallel model. Also, these simulations will provide numerous algorithms for ASC by providing an automatic method ofconverting algorithms from PRAM to ASC.
Routing on the PADAM: Degrees of Optimality
, 1997
"... Routing problems are studied for the Parallel AlternatingDirection Access Machine. The goal is to investigate what level of optimality can be achieved depending on loads of packets per memory unit. In the case of typical moderate loads, our algorithms are optimal to within a small multiplicative co ..."
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Cited by 3 (3 self)
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Routing problems are studied for the Parallel AlternatingDirection Access Machine. The goal is to investigate what level of optimality can be achieved depending on loads of packets per memory unit. In the case of typical moderate loads, our algorithms are optimal to within a small multiplicative constant; a deterministic and a randomized algorithm are developed, both faster than the best previously known routing algorithm. Moreover, for sufficiently large loads, an algorithm which misses optimality by only an additive lowerorder term is designed. We consider also offline routing problems, and multidimensional extension of the model. 1 Introduction The Parallel AlternatingDirection Access Machine, PADAM, is a multiprocessor computer with memory units, MUs, arranged in a grid structure, together with the processing units, PUs. The twodimensional n \Theta n PADAM has n PUs and n 2 MUs arranged according to the pattern in Figure 1 (notice that there are only n PUs: the PUs marked...
Geometric Approach for Optimal Routing on Mesh with Buses
 PROC. 7TH IEEE SYMP. PARALLEL DISTRIB. COMPUT
, 1995
"... The architecture of 'mesh of buses' is an important model in parallel computing. Its main advantage is that the additional broadcast capability can be used to overcome the main disadvantage of the mesh, namely its relatively large diameter. We show that the addition of buses indeed acce ..."
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Cited by 2 (1 self)
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The architecture of 'mesh of buses' is an important model in parallel computing. Its main advantage is that the additional broadcast capability can be used to overcome the main disadvantage of the mesh, namely its relatively large diameter. We show that the addition of buses indeed accelerates routing times. Furthermore, unlike in the `store and forward' model, the routing time becomes proportional to the network load, resulting in decreasing in routing time for a smaller number of packets. We consider 11 routing of m packets in a ddimensional mesh with n d processors and d \Delta n d\Gamma1 buses (one per row and column). The two standard models of accessing the buses are considered and compared: CREW, in which only one processor may transmit at any given time on a given bus, and the CRCW model in which several processors may attempt to transmit at the same time (getting a noise signal as a result). We design a routing algorithm that routes m packets in the CREW model ...
Scheduling Lighttrails on WDM Rings
"... Abstract—We consider the problem of scheduling communication on optical WDM (wavelength division multiplexing) networks using the lighttrails technology. We give two online algorithms which we prove to have competitive ratios O(log n) and O(log 2 n) respectively. We also consider a simplification o ..."
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Cited by 1 (1 self)
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Abstract—We consider the problem of scheduling communication on optical WDM (wavelength division multiplexing) networks using the lighttrails technology. We give two online algorithms which we prove to have competitive ratios O(log n) and O(log 2 n) respectively. We also consider a simplification of the problem in which the communication pattern is fixed and known before hand, for which we give a solution using O(c + log n) wavelengths, where c is the congestion and a lower bound on the number of wavelengths needed. While congestion bounds are common in communication scheduling, and we use them in this work, it turns out that in some cases they are quite weak. We present a communication pattern for which the congestion bound is O(log n / log log n) factor worse than the best lower bound. In some sense this pattern shows the distinguishing character of lighttrail scheduling. Finally we present simulations of our online algorithms under various loads. I.
(l, k)Routing on Plane Grids
 JOURNAL OF INTERCONNECTION NETWORKS
, 2009
"... The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the (`, k)routing problem, each node can send at most ` packets and receive at most k packets. Permutation rou ..."
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Cited by 1 (0 self)
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The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the (`, k)routing problem, each node can send at most ` packets and receive at most k packets. Permutation routing is the particular case ` = k = 1. In the rcentral routing problem, all nodes at distance at most r from a fixed node v want to send a packet to v. In this article we study the permutation routing, the rcentral routing and the general (`, k)routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We use the storeandforward ∆port model, and we consider both full and halfduplex networks. We first survey the existing results in the literature about packet routing, with special emphasis on (`, k)routing on plane grids. Our main contributions are the following: 1. Tight permutation routing algorithms on fullduplex hexagonal grids, and half duplex triangular and hexagonal grids. 2. Tight rcentral routing algorithms on triangular and hexagonal grids.