The New Class of g-Chain Periodic Sorters

Aperiodic sorteris a sorting network that is a cascade of a number of identicalblocks, where outputiof each block is inputiof the next block. Previously, Dowd, Perl, Rudolph, and Saks introduced thebalancedmerging network, withN=2^kinputs/outputs and log Nstages of comparators. Using a very intricate proof, they showed that a cascade of log Nsuch blocks constitutes a sorting network. In this paper, we introduce a large class of merging networks with the same periodic property. This class contains 2^N/2−1networks, whereN=2^kis the number of inputs. The balanced merger is one network in this class. Other networks use fewer comparators. We provide a very simple and elegant correctness proof based on the recursive structure of the networks.     

The design of complete encryption networks using cryptographically equivalent permutations

A design procedure for complete substitution-permutation encryption networks is presented. The cryptographically important property of completeness is achieved after three iterations, the minimum possible number for all networks of size N = i · n² (i = 1,2,…,n), where n is the size of the substitution function used. The permutation stage is constructed by choosing a single member of a class of cryptographically equivalent permutations for all the network rounds, hence having the advantage of simplifying the network implementation. An algorithm for generating members of the class of cryptographically equivalent permutations is given.     

基于二进制寻路法和多Omega网络的自路由无阻塞多级网

提出了一种可以无阻塞地传输其输入与输出间任意多播信号的新型自路由无阻塞多级网。该网络采用了循环重建法,以二进制扩散概念为基础。它由一个二进制扩散网络和两个二分之一大小的多播路由网络循环构建而成。多播信号由第一个Omega网复制并二分扩散到输出端口,进入N×N的Omega×Omega-1网络,再进入紧随其后的N/2×N/2的Omega×Omega-1网络……。每个Omega×Omega-1网络负责依照目的地址的有效标志位将输入置换到输出的上半部分和下半部分,再分别进入上下两个子Omega×Omega-1网络中做同样的处理,如此类推,直到全部地址有效位处理完毕,从而完成自路由无阻塞的多播传输。由于各大小不等的Omega×Omega-1网络皆可并行设置和并行路由,故此种新型多Omega网络的设置时间为O(NlogN),路由时间为O(log2N),硬件代价则为O(Nlog2N)。它比现行已知的多播网络设计具有较优的代价。     

Laying Out the Interconnection Network of the Transpose Bijection

A subnetwork which performs the transpose bijection was used by Clos and others in the construction of interconnection networks. We consider the laying out of this subnetwork on the rectilinear grid. It is assumed that the N = n ² inputs are arranged on one straight line, the N outputs on a parallel line and the connections are laid out in between. It is shown how this can be done in grid area 1/2 N ² + o(N ² ) , which is essentially optimal. One of the consequences of this result is that the butterfly network with N = 2 ^2l input and output lines can also be laid out (optimally) in grid area 1/2 N ² + o(N ² ) .     

A generalization of the 0-1 principle for sorting

The traditional zero-one principle for sorting networks states that “if a network with n input lines sorts alln² binary sequences into nondecreasing order, then it will sort any arbitrary sequence of n numbers into nondecreasing order”. We generalize this to the situation when a network sorts almost all binary sequences and relate it to the behavior of the sorting network on arbitrary inputs. We also present an application to mesh sorting.     

Scheduling Protocols for Switches with Large Envelopes

Traditionally, switches make scheduling decisions on the granularity of a packet. However, this is becoming increasingly difficult since network bandwidth is growing rapidly whereas packet sizes remain largely unchanged. Therefore the service time of an individual packet is decreasing rapidly. In this paper we study switches that make scheduling decisions on the granularity of an envelope which can be much larger than a packet in size. For an output-queued switch with envelope size E, each output chooses one input every E time steps and transmits packets from this chosen input during the next E steps. For an input-queued switch with envelope size E, one matching from the inputs to the outputs is computed every E steps and only the input–output pairs that are defined by this matching are allowed to transmit packets during the next E steps. Traditional switches correspond to envelope size E = 1 and almost all previous scheduling work deals with this case exclusively. We first show how some stable protocols for scheduling networks of output-queued switches with E = 1 fail for arbitrary E when these protocols are generalized in the most straightforward manner. We then present an extremely simple protocol that does guarantee network stability for output-queued switches for any E ≥ 1. For input-queued switches we first present a max-weight matching protocol that is stable for a single switch with arbitrary E. We then present a more complex protocol that achieves stability for a network of input-queued switches for any E ≥ 1.     

LEFT TO RIGHT PARSING OF LEXICALIZED TREE-ADJOINING GRAMMARS1

This paper presents an algorithm (a parser) for analyzing sentences according to grammatical constraints expressed in the framework of lexicalized tree-adjoining grammar. For the current grammars of English, the algorithm behaves much better and requires much less time than its worst-case complexity. The main objective of this work is to design a practical parser whose average-case complexity is much superior to its worst case. Most of the previous methods always required the worst-case complexity. The algorithm can be used in two modes. As a recognizer it outputs whether the input sentence is grammatically correct or not. As a parser it outputs a detailed analysis of the grammatically correct sentences. As sentences are read from left to right, information about possible continuations of the sentence is computed. In this sense, the algorithm is called a predictive left to right parser. This feature reduces the average time required to process a given sentence. In the worst case, the parser requires an amount of time proportional to G²n⁶ for a sentence of n words and for a lexicalized tree-adjoining grammar of size G. The worst-case complexity is only reached with pathological (not naturally occurring) grammars and inputs.     

A Scalable Interconnection Network Architecture for Petaflops Computing

Extrapolating technology advances in the near future, a computer architecture capable of petaflops performance will likely be based on a collection of processing nodes interconnected by a high-performance network. One possible organization would consist of thousands of inexpensive, low-power symmetric multiprocessor (SMP) nodes. Each node will inject data into the interconnection network at a very large rate and consequently, the interconnect scheme is one of the most crucial design issues affecting system performance. This paper describes the 2D simultaneous optical multiprocessor exchange bus (2D SOME-Bus) which has the potential to become the basis of a high-end computer architecture capable of petaflops performance. It consists of N horizontal, N vertical 1D SOME-Bus networks, and N ² nodes. Each node is connected to one horizontal and one vertical 1D SOME-Bus. Each of N nodes connected to one 1D SOME-Bus has a dedicated broadcast channel and an input channel interface based on an array of N receivers monitoring all N channels and allowing multiple simultaneous broadcasts. In the 2D SOME-Bus, messages being broadcast on one Bus can be broadcast in a cut-through manner on one or more Buses in the other dimension. This paper describes the optoelectronic devices and technology which make the 2D SOME-Bus possible, and the network interface organization. It also presents simulation results which compare the performance of the 2D SOME-Bus, the 1D SOME-Bus, the crossbar and the torus under the message-passing paradigm.     

On necessary conditions for scale-freedom in complex networks,with applications to computer communication systems

Many complex networks exhibit a scale-free, power-law distribution of vertex degrees. This common feature is a consequence of two generic mechanisms relating to the formation of real networks: (i) networks tend to expand over time through the addition of new vertices and (ii) new vertices attach preferentially to those that are already well connected. We show that for many natural or man-made complex networks possessing a scale-free power-law distribution with the exponent γ ≥ 2, the number of degree-1 vertices, when nonzero, is of the same order as the network size N and that the average degree is of order at most log N. Our results expose another necessary characteristic of such networks. Furthermore, our method has the benefit of relying only on conditions that are static and easily verified for arbitrary networks. We use the preceding results to derive a closed-form formula approximating the distance distribution in scale-free networks. Such distributions are applied extensively in the fields of computer communication and software architecture, among other domains.     

相接行凸约束网络的快速识别算法

约束网络为计算机科学中的许多问题提供了一种有效的表示方法.一般而言,约束满足问题是NP完全的.然而,许多实际问题通常对约束的结构或形式施加了特殊的限制,从而能够高效地加以解决.迄今,为了识别易处理约束类,人们对特殊的约束或约束网络方面进行了许多研究.相接行凸(connected row-convex,简称CRC)约束网络是Deville等人提出的一类易处理问题.为了给该类问题寻求有效的快速识别算法,在CRC约束网络相关工作基础上,提出了CRC约束矩阵的标准型.在分析CRC约束矩阵的标准型性质的基础上,利用行凸(row-convex,简称RC)约束网络的判定,结合PQ树(由P节点和Q节点构成的树)的性质和矩阵的索引表示法,给出了CRC约束网络的快速识别算法.该算法的时间复杂度为O(n³d²),其中,n为约束网络涉及的变量数,d为各变量的定义域中最大定义域的大小.该时间复杂度达到该类问题的最佳时间复杂度,从而为实际的CRC约束满足问题的求解提供了可行的方法.     

A Study of Permutation Networks: New Designs and Some Generalizations

Permutation networks have been used in the literature to model interprocessor and processor-memory interconnections in parallel computers. This paper introduces new permutation network designs and generalizes the notion of a permutation network to provide a more flexible model of such interconnections. The new designs are based concentrators and superconcentrators, and for n inputs they can be optimized to obtain self-routing permutation networks with O(n lg n) cost, O(lg n) depth, and O(lg²n) routing time. The main feature of these new network designs is that they do not require complex routing schemes such as Clos networks since they are inherently self-routing. Generalizations of these designs are also given to obtain permutation networks in which the numbers of inputs and outputs may be different, and/or the maximum number of parallel routes between inputs and outputs can be less than the number of inputs or outputs, or both. For n inputs, αn outputs, and O(n^ϵ) parallel routes, where 0 < α ≤ 1, 0 < ϵ < 1, these generalized designs can be optimized to have permutation networks with O(n) cost, O(lg n), depth, and O(lg²n) routing time. It is shown that the previously known designs, such as Clos networks, result in inferior realizations when compared with these new designs.     

Neural network application for direct feedback controllers

The author presents a learning algorithm and capabilities of perceptron-like neural networks whose outputs and inputs are directly connected to plants just like ordinary feedback controllers. This simple configuration includes the difficulty of teaching the network. In addition, it is preferable to let the network learn so that a global and arbitrary evaluation of the total responses of the plant will be optimized eventually. In order to satisfy these needs, genetic algorithms are modified to accommodate the network learning procedure. This procedure is a kind of simulated evolution process in which a group of networks gradually improves as a whole, by crossing over connection weights among them, or by mutational changes of the weights, according to fitness values assigned to each network by a global evaluation. Simulations demonstrate that these networks can be optimized in terms of various evaluations, and they can discover schemes by themselves, such as state estimation and nonlinear control.     

Probabilistic design of layered neural networks based on theirunified framework

Proposes three ways of designing artificial neural networks based on a unified framework and uses them to develop new models. First, the authors show that artificial neural networks can be understood as probability density functions with parameters. Second, the authors propose three design methods for new models: a method for estimating the occurrence probability of the inputs, a method for estimating the variance of the outputs, and a method for estimating the simultaneous probability of inputs and outputs. Third, the authors design three new models using the proposed methods: a neural network with occurrence probability estimation, a neural network with output variance estimation, and a probability competition neural network. The authors' experimental results show that the proposed neural networks have important abilities in information processing; they can tell how often a given input occurs, how widely the outputs are distributed, and from what kinds of inputs a given output is inferred.     

New Bounds on the Size of Optimal Meshes

The theory of optimal size meshes gives a method for analyzing the output size (number of simplices) of a Delaunay refinement mesh in terms of the integral of a sizing function over the input domain. The input points define a maximal such sizing function called the feature size. This paper presents a way to bound the feature size integral in terms of an easy to compute property of a suitable ordering of the point set. The key idea is to consider the pacing of an ordered point set, a measure of the rate of change in the feature size as points are added one at a time. In previous work, Miller et al. showed that if an ordered point set has pacing ?, then the number of vertices in an optimal mesh will be O(?^dn), where d is the input dimension. We give a new analysis of this integral showing that the output size is only θ(n+nlog?). The new analysis tightens bounds from several previous results and provides matching lower bounds. Moreover, it precisely characterizes inputs that yield outputs of size O(n).     

Parallel algorithms for routing in nonblocking networks

We construct nonblocking networks that are efficient not only as regards their cost and delay, but also as regards the time and space required to control them. In this paper we present the first simultaneous weakly optimal solutions for the explicit construction of nonblocking networks, the design of algorithms and data-structures. Weakly optimal is in the sense that all measures of complexity (size and depth of the network, time for the algorithm, space for the data-structure, and number of processor-time product) are within one or more logarithmic factors of their smallest possible values. In fact, we construct a scheme in which networks withn inputs andn outputs have sizeO(n(logn)²) and depthO(logn), and we present deterministic and randomized on-line parallel algorithms to establish and abolish routes dynamically in these networks. In particular, the deterministic algorithm usesO((logn)⁵) steps to process any number of transactions in parallel (with one processor per transaction), maintaining a data structure that useO(n(logn)²) words.     

Differential flatness of two one-forms in arbitrary number of variables

Given a differentially flat system of ODEs, flat outputs that depend only on original variables but not on their derivatives are called zero-flat outputs and systems possessing such outputs are called zero-flat. In this paper we present a theory of zero-flatness for a system of two one-forms in arbitrary number of variables (t,x¹,…,x^N). Our approach splits the task of finding zero-flat outputs into two parts. First part involves solving for distributions that satisfy a set of algebraic conditions. The second part involves finding an integrable distribution from the solution set of the first part. Typically this part involves solving PDEs. Our results are also applicable in determining if a control affine system in n states and n−2 controls has flat outputs that depend only on states. We illustrate our method by examples.     

Deterministic broadcasting in ad hoc radio networks

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multi-hop networks. We study the time of deterministic broadcasting under this scenario. For the model without collision detection, we develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary n-node graphs, working in time . Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop efficient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs. Received: January 2000 / Accepted: June 2001     

Optimal extraction of motif patterns in 2D

The combinatorial explosion of motif patterns occurring in 1D and 2D arrays leads to the consideration of special classes of motifs growing linearly with the size of the input array. Such motifs, called irredundant motifs, are able to succinctly represent all of the other motifs occurring in the same array within reasonable time and space bounds. In previous work irredundant motifs were extracted from 2D arrays in O(N²log²nloglogn) and O(N³) time, where N is the size of the 2D input array and n is its largest dimension.In this paper, we present an algorithm to extract irredundant motifs from 2D arrays that is quadratic in the size of the input. The input is defined on a binary alphabet. It is shown that the algorithm is optimal and practically faster than the previous ones.     

Acknowledged broadcasting in ad hoc radio networks

We consider ad hoc radio networks in which each node knows only its own identity but is unaware of the topology of the network, or of any bound on its size or diameter. Acknowledged broadcasting (AB) is a communication task consisting in transmitting a message from a distinguished source to all other nodes of the network and making this fact common knowledge among all nodes. To do this, the underlying directed graph must be strongly connected. Working in a model allowing all nodes to transmit spontaneously even before getting the source message, Chlebus et al. [B. Chlebus, L. Ga?sieniec, A. Gibbons, A. Pelc, W. Rytter, Deterministic broadcasting in unknown radio networks, Distrib. Comput. 15 (2002) 27-38] proved that AB is impossible, if collision detection is not available, and gave an AB algorithm using collision detection that works in time O(nD) where n is the number of nodes and D is the eccentricity of the source. Uchida et al. [J. Uchida, W. Chen, K. Wada, Acknowledged broadcasting and gossiping in ad hoc radio networks, Theoret. Comput. Sci. 377 (2007) 43-54] showed an AB algorithm without collision detection working in time O(n4/3log10/3n) for all strongly connected networks of size at least 2. In particular, it follows that the impossibility result from [B. Chlebus, L. Ga?sieniec, A. Gibbons, A. Pelc, W. Rytter, Deterministic broadcasting in unknown radio networks, Distrib. Comput. 15 (2002) 27-38] is really caused by the singleton network for which AB amounts to realize that the source is alone. We improve those two results by presenting two generic AB algorithms using a broadcasting algorithm without acknowledgement, as a procedure. For a large class of broadcasting algorithms the resulting AB algorithm has the same time complexity. Using the currently best known broadcasting algorithms, we obtain an AB algorithm with collision detection working in time O(min{nlog²D,nlognloglogn}), for arbitrary strongly connected networks, and an AB algorithm without collision detection working in time O(nlognloglogn) for all strongly connected networks of size n?2. Moreover, we show that in the model in which only nodes that already got the source message can transmit, AB is infeasible in a strong sense: for any AB algorithm there exists an infinite family of networks for which this algorithm is incorrect.     

A Neural Algorithm for the Maximum Clique Problem: Analysis,Experiments, and Circuit Implementation

{In this paper we design and analyze a neural approximation algorithm for the Maximum Clique problem. This algorithm, having as input an arbitrary undirected graph G = \langle V, E\rangle , constructs a finite sequence of Hopfield networks such that the attractor of the last network in the sequence represents a maximal clique of G . We prove that D(G) ⋅ |E ^{\rm c} | , where D(G) = max _{{i,j}\notin E} \min{d _i , d _j } , d _i is the degree of the vertex i of G , and |E ^{\rm c} | denotes the cardinality of the set of edges in the complement graph, is an upper bound to the number of the networks in the sequence. Some experiments made on the second DIMACS benchmark and on random graphs show that: 1. The quality of the solutions found by the algorithm is satisfactory. 2. The theoretical upper bound D(G) ⋅ |E ^{\rm c} | is quite pessimistic. For random graphs we propose an empirical formula that gives a better estimate of the number of networks in the sequence. Moreover, thanks to the simplicity of the algorithm, we are able to design a uniform family of circuits of small size (\approx 10n ² log ₂ n ) that implements it. The circuit, which solves the problems for graphs of at most 32 vertices, has then been programmed on FPGAs (Field Programmable Gate Arrays). An analysis in terms of size and time complexity is given. Received November 10, 1998; revised December 2000.