Deterministic Communication in Radio Networks with Large Labels

We study deterministic gossiping in ad hoc radio networks with large node labels. The labels (identifiers) of the nodes come from a domain of size N which may be much larger than the size n of the network (the number of nodes). Most of the work on deterministic communication has been done for the model with small labels which assumes N = O(n). A notable exception is Peleg's paper, where the problem of deterministic communication in ad hoc radio networks with large labels is raised and a deterministic broadcasting algorithm is proposed, which runs in O(n²log n) time for N polynomially large in n. The O(nlog²n)-time deterministic broadcasting algorithm for networks with small labels given by Chrobak et al. implies deterministic O(n log N log n)-time broadcasting and O(n²log²N log n)-time gossiping in networks with large labels. We propose two new deterministic gossiping algorithms for ad hoc radio networks with large labels, which are the first such algorithms with subquadratic time for polynomially large N. More specifically, we propose: a deterministic O(n^3/2log²N log n)-time gossiping algorithm for directed networks; and a deterministic O(n log²N log²n)-time gossiping algorithm for undirected networks.     

Energy-Efficient Wireless Network Design

A crucial issue in wireless networks is to support efficiently communication patterns that are typical in traditional (wired) networks. These include broadcasting, multicasting, and gossiping (all-to-all communication). In this work we study such problems in static ad hoc networks. Since, in ad hoc networks, energy is a scarce resource, the important engineering question to be solved is to guarantee a desired communication pattern minimizing the total energy consumption. Motivated by this question, we study a series of wireless network design problems and present new approximation algorithms and inapproximability results.     

Communication Complexity of Gossiping by Packets

This paper considers the problem of gossiping with packets of limited size in a network with a cost function. We show that the problem of determining the minimum cost necessary to perform gossiping among a given set of participants with packets of limited size is NP-hard. We also give an approximate (with respect to the cost) gossiping algorithm. The ratio between the cost of an optimal algorithm and the approximate one is less than 1 + 2(k− 1)/n, wherenis the number of nodes participating in the gossiping process andk≤n− 1 is the upper bound on the number of individual blocks of information that a packet can carry. We also analyze the communication time and communication complexity, i.e., the product of the communication cost and time, of gossiping algorithms.     

ANALYSIS OF GOSSIPING ALGORITHMS WITH RESTRICTED BUFFERS

In this paper we present a new algorithm for gossiping in distributed-memory parallel architectures whose interconnection network is a two-dimensional torus. The results are presented for odd-sized square torus, but the extensions are discussed at the end of the paper. The gossiping communication routine corresponds to simultaneous broadcasts at each node. In this study we assume a store-and-forward routing mechanism where all processors send a message of same length on each link during the time step. As we briefly discuss at the end, this holds also for circuit-switched routing for large messages.

The main result of this work is to establish a general lower bound for gossiping in a square torus and to analyze the influence of buffering. After a brief discussion of the existing solutions, we present the principle of a new algorithm. Then, we study its complexity with restricted buffers. This new algorithm is compared with the existing gossiping algorithms from its buffering capabilities and is found to be superior.     

Optimal information dissemination in star and pancake networks

This paper presents a new decomposition technique for hierarchical Cayley graphs. This technique yields a very easy implementation of the divide and conquer paradigm for some problems on very complex architectures as the star graph or the pancake. As applications, we introduce algorithms for broadcasting and prefix-like operations that improve the best known bounds for these problems. We also give the first nontrivial optimal gossiping algorithms for these networks. In star-graphs and pancakes with N=n! processors, our algorithms take less than [log N]+1.5n steps     

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.     

一个新的分布式最小连通支配集近似算法

在计算机网络中广泛使用广播来解决一些网络问题,设计有效的广播算法是一项重要的课题。文中提出一种分布地计算网络最小连通支配集的近似算法并给出了它的正确性证明。它只需要网络节点具有局部的网络状态信息,可伸缩性强。通过此算法可以在网络中自动形成一个虚拟骨干网,从而可为网络中的广播和路由操作提供一个有效的通信基础。模拟结果表明,文中提出的算法求得的连通支配集小,能较好地应用于一般网络以及移动自组网络中。     

Optimal all-to-all personalized exchange in self-routablemultistage networks

All-to-all personalized exchange is one of the most dense collective communication patterns and occurs in many important applications in parallel computing. Previous all-to-all personalized exchange algorithms were mainly developed for hypercube and mesh/torus networks. Although the algorithms for a hypercube may achieve optimal time complexity, the network suffers from unbounded node degrees and thus has poor scalability in terms of I/O port limitation in a processor. On the other hand, a mesh/torus has a constant node degree and better scalability in this aspect, but the all-to-all personalized exchange algorithms have higher time complexity. In this paper, we propose an alternative approach to efficient all-to-all personalized exchange by considering another important type of networks, multistage networks, for parallel computing systems. We present a new all-to-all personalized exchange algorithm for a class of unique-path, self-routable multistage networks. We first develop a generic method for decomposing all-to-all personalized exchange patterns into some permutations which are realizable in these networks, and then present a new all-to-all personalized exchange algorithm based on this method. The newly proposed algorithm has O(n) time complexity for an n×n network, which is optimal for all-to-all personalized exchange. By taking advantage of fast switch setting of self-routable switches and the property of a single input/output port per processor in a multistage network, we believe that a multistage network could be a better choice for implementing all-to-all personalized exchange due to its shorter communication latency and better scalability     

Study of General Icomplete Star Interconnection Networks

The star networks,which were originally proposed by Akers and Harel,have suffered from a rigorous restriction on the number of nodes.The general incomplete star networks(GISN) are proposed in this paper to relieve this restriction.An efficient labeling scheme for GISN is given,and routing and broadcasting algorithms are also presented for GIS.The communication diameter of GISN is shown to be bounded by 4n-7.The proposed single node broadcasting algorithm is optimal with respect to time complexity O(nlog2n).     

双环Petersen图互联网络及路由算法

Petersen图由于具有短直径和正则性等特性,因此在并行与分布式计算中具有良好的性能.基于双环结构,构造了一个双环Petersen图互联网络DLCPG(k).同时,分别设计了DLCPG(k)上的单播、广播和容错路由算法.证明了DLCPG(k)不但具有良好的可扩展性、短的网络直径和简单的拓扑结构等特性,而且对于10k个节点组成的互联网络,DLCPG(k)还具有比二维Torus以及RP(k)互联网络更小的直径和更优越的可分组性.另外,还证明了其上的单播、广播路由算法的通信效率与RP(k)上的单播和广播路由算法的通信效率相比均有明显的提高.仿真实验表明,新的容错路由算法也具有良好的容错性能.     

基于k 最短路由的mesh光网络p圈构造方法*

Pcycle是mesh光网络中一种十分优秀的保护算法,圈构造算法是p圈法设计的前提。首先介绍了圈的概念及常见圈构造算法和基于k最短路由的p圈启发式算法,提出了基于k最短路改进metaDijkstra的圈构造算法。实验仿真表明该方案比较适合网状光网络中的圈构造。     

Shifting gears: Changing algorithms on the fly to expedite Byzantine agreement

We describe several new algorithms for Byzantine agreement. The first of these is a simplification of the original exponential-time Byzantine agreement algorithm due to Pease, Shostak, and Lamport, and is of comparable complexity to their algorithm. However, its proof is very intuitively appealing. A technique of shifting between algorithms for solving the Byzantine agreement problem is then studied. We present two families of algorithms obtained by applying a shift operator to our first algorithm. These families obtain the same rounds to message length trade-off as do Coan's families but do not require the exponential local computation time (and space) of his algorithms. We also describe a modification of an -resilient algorithm for Byzantine agreement of Dolev, Reischuk, and Strong. Finally, we obtain a hybrid algorithm that dominates all our others, by beginning execution of an algorithm in one family, first shifting into an algorithm of the second family, and finally shifting into an execution of the adaptation of the Dolev, Reischuk, and Strong algorithm.     

最优并行算法评价标准的研究

加速比是判断一个并行虎法是否最优的依据，但播送类问题是针对并行机提出的，不存在串行算法，加速比标准对之无能为力，通过对几种不同并行计算模型上播送算法的研究，文中提出了一个不依赖于上体模型的一般化的评价标准ｍｉｎＣ＾２用以判断播送算法是否最优，为这类问题的进一步工辟了新的思路。     

Modeling gossip-based content dissemination and search in distributed networking

This paper presents a rigorous analytic study of gossip-based message dissemination schemes that can be employed for content/service dissemination or discovery in unstructured and distributed networks. When using random gossiping, communication with multiple peers in one gossiping round is allowed. The algorithms studied in this paper are considered under different network conditions, depending on the knowledge of the state of the neighboring nodes in the network. Different node behaviors, with respect to their degree of cooperation and compliance with the gossiping process, are also incorporated. From the exact analysis, several important performance metrics and design parameters are analytically determined. Based on the proposed metrics and parameters, the performance of the gossip-based dissemination or search schemes, as well as the impact of the design parameters, are evaluated.     

Efficient communication primitives on hypercubes

We give practical algorithms, complexity analysis and implementation for one-to-all broadcasting, all-to-all personalized communication and matrix transpose (with two-dimensional partitioning of the matrix) on hypercubes. We assume the following communication characteristics: circuit-switched, e-cube routing and one-port communication model. For one-to-all broadcasting, we give an algorithm that combines the well-known recursive doubling algorithm[1] and the algorithm based on edgedisjoint spanning trees[2]. The measured times of the combined algorithm are always superior to those of the edge-disjoint spanning tree algorithm and outperform the recursive doubling algorithm. For all-to-all personalized communication we propose a hybrid algorithm that combines the well-known recursive doubling algorithm[3,4] and the recently proposed direct-route algorithm[5,6] Our hybrid algorithm balances between data transfer time and start-up time of these two algorithms, and its communication complexity is estimated to be better than the two previous algorithms for a range of machine parameters. For matrix transpose with two-dimensional partitioning of the matrix, we relate a two-phase algorithm to the previous result in Reference 7. The algorithm is predicted to be better than the recursive transpose algorithm[8] by n nearest-neighbor communications[4]. It takes advantage of circuit-switched routing and is congestion-free within each phase. We also suggest a way of storing the matrix such that the transpose operation can be realized in one phase without congestion.     

An O(n 1.5 ) Deterministic Gossiping Algorithm for Radio Networks

We consider the problem of distributed gossiping in radio networks of unknown topology. For radio networks of size n and diameter D , we present an adaptive deterministic gossiping algorithm of time O ($\sqrt{D}$ n+n log 2 n ) or O(n 1.5) . This algorithm is a tuned version of the fastest previously known gossiping algorithm due to Gasieniec and Lingas [1], and improves the time complexity by a poly-logarithmic factor.     

Gossiping on meshes and tori

Algorithms for performing gossiping on one- and higher-dimensional meshes are presented. As a routing model, the practically important wormhole routing is assumed. We especially focus on the trade-off between the start-up time and the transmission time. For one-dimensional arrays and rings, we give a novel lower bound and an asymptotically optimal gossiping algorithm for all choices of the parameters involved. For two-dimensional meshes and tori, a simple algorithm composed of one-dimensional phases is presented. For an important range of packet and mesh sizes, it gives clear improvements upon previously developed algorithms. The algorithm is analyzed theoretically and the achieved improvements are also convincingly demonstrated by simulations, as well as an implementation on the Paragon. On the Paragon, our algorithm even outperforms the gossiping routine provided in the NX message-passing library. For higher-dimensional meshes, we give algorithms which are based on an interesting generalization of the notion of a diagonal. These algorithms are analyzed theoretically, as well as by simulation     

Optimal Communication Primitives on the Generalized Hypercube Network

Efficient interprocessor communication is crucial to increasing the performance of parallel computers. In this paper, a special framework is developed on thegeneralized hypercube, a network that is currently receiving considerable attention. Using this framework as the basic tool, a number of spanning subgraphs with special properties to fit various communication needs are constructed on the network. The importance of these spanning subgraphs is demonstrated with the development of optimal algorithms for four fundamental communication problems, namely, theone-to-allandall-to-all broadcastingand theone-to-allandall-to-all scattering. Broadcastingis the distribution of the same group of messages from a source processor to all other processors, andscatteringis the distribution of distinct groups of messages from a source processor to each other processor. We consider broadcasting and scattering from a single processor of the network (one-to-all broadcasting and scattering) and simultaneously from all processors of the network (all-to-all broadcasting and scattering). For the all-to-all broadcasting and scattering algorithms, a special technique is developed on the generalized hypercube so that messages originating at individual nodes are interleaved in such a manner that no two messages contend for the same edge at any given time. The communication problems are studied under thestore-and-forward, all-portcommunication model. Lower bounds are derived for the above problems under the stated assumptions, in terms of time and number of message transmissions, and optimal algorithms are designed.     

Study of General Incomplete Star Interconnection Networks

IIntroduct1OllThe star graph【1]proposed as a particular case ofC叫ley graphs[ZJ Is vertex－and edge－symmetric．strongly hlerarchlcal,maximally tault－tolerant,strongly resilient and has diameter and node degreethat are superior to those of a slmll。－slied hypercube(which Is also a Cnyley graph)IOr parallelcomputers[3]．MNor references can be found In studying the star graph regarding its propertiesllJ,e毗edding cwabllity[4],communication c叩劝ility[5－71,andfanfaut－toierm尬 cap劝ility…     

适用于区块链的高效异步拜占庭容错算法

针对现有异步共识算法存在的多轮次通信开销大、随机抽签算法中缺乏信誉机制导致了较多的抽取次数等不足,提出了一种高效的异步拜占庭容错算法PenguinBFT。首先,在广播交易时直接广播原文,降低了共识通信开销;其次,引入了节点信誉评估机制,从网络情况相对稳定的节点集合中选取出块者,以减少随机抽取次数;最后,对网络节点进行分区,在请求交易缺失时,让不同的节点访问不同的分区进行交易恢复,既能减少通信开销又能提升交易恢复效率。实验结果表明,当节点规模达到64时,提出的PenguinBFT算法相较于Honey-BadgerBFT、DumboBFT和DispersedLedger算法,在通信开销、吞吐量和交易确认时延等方面均有50%以上的提升。