Families of consensus algorithms

The tiny encryption algorithm (TEA) is widely used when performing dissipative particle dynamics (DPD) calculations in parallel, usually on distributed memory systems. In this research, we reduced the computational cost of the TEA hash function and investigated the influence of the quality of the random numbers generated on the results of DPD calculations. It has already been established that the randomness, or quality, of the random numbers depend on the number of processes from internal functions such as SHIFT, XOR and ADD, which are commonly referred to as "rounds". Surprisingly, if we choose seed numbers from high entropy sources, with a minimum number of rounds, the quality of the random numbers generated is sufficient to successfully perform accurate DPD simulations. Although it is well known that using a minimal number of rounds is insufficient for generating high-quality random numbers, the combination of selecting good seed numbers and the robustness of DPD simulations means that we can reduce the random number generation cost without reducing the accuracy of the simulation results.

The problem of optimal scheduling n tasks in a parallel processor system is studied. The tasks are malleable, i.e., a task may be executed by several processors simultaneously and the processing speed of a task is a nonlinear function of the number of processors allocated to it. The total number of processors is m and it is an upper bound on the number of processors that can be used by all the tasks simultaneously. It is assumed that the number of processors is sufficient to process all the tasks simultaneously, i.e. n≤m. The objective is to find a task schedule and a processor allocation such that the overall task completion time, i.e. the makespan, is minimized. The problem is motivated by real-life applications of parallel computer systems in scientific computing of highly parallelizable tasks. An O(n) algorithm is presented to solve this problem when all the processing speed functions are convex. If these functions are all concave and the number of tasks is a constant, the problem can be solved in polynomial time. A relaxed problem, in which the number of processors allocated to each task is not required to be integer, can be solved in O(nmax {m,nlog 2 m}) time. It is proved that the minimum makespan values for the original and relaxed problems coincide. For n=2 or n=3, an optimal solution for the relaxed problem can be converted into an optimal solution for the original problem in a constant time.

With the rapid advancement of wireless networking technology, networks have evolved from static to dynamic. Reliability of dynamic networks has virtually become an important issue. Fortunately, a solution to the above issue can be derived from solutions to the Byzantine Agreement (BA) problem. BA problem can be solved by protocols that make processors reach an agreement through message exchange. Protocols used to solve the problem can be divided into Immediate Byzantine Agreement (IBA) protocols and Eventual Byzantine Agreement (EBA) protocols. In IBA protocols, the number of rounds of message exchange is determined by the total number of processors in the network. Even if no faulty processor is present in the network, IBA protocols still require a fixed number of rounds of message exchange, causing a waste of time. In contrast, EBA protocols dynamically adjust the number of rounds of message exchange according to the interference of faulty processors. In terms of efficiency, EBA protocols certainly outperform IBA protocols. Due to the fact that the existing EBA protocols have been designed for static networks, they cannot work on dynamic networks. In this paper, we revisit the EBA problem in dynamic networks to increase the reliability of dynamic networks. Simulations will be conducted to validate that the proposed protocol requires the minimum rounds of message exchange and can tolerate the maximum number of malicious faulty processors compared to other existing protocols.

We present a randomized parallel list ranking algorithm for distributed memory multiprocessors, using a BSP type model. We first describe a simple version which requires, with high probability, log(3p)+log ln(n)=O(logp+log logn) communication rounds (h-relations withh=O(n/p)) andO(n/p)) local computation. We then outline an improved version that requires high probability, onlyr⩽(4k+6) log(2/3p)+8=O(k logp) communication rounds wherek=min{i⩾0 |ln(i+1)n⩽(2/3p)2i+1}. Notek<ln*(n) is an extremely small number. Forn andp⩾4, the value ofk is at most 2. Hence, for a given number of processors,p, the number of communication rounds required is, for all practical purposes, independent ofn. Forn⩽1, 500,000 and 4⩽p⩽2048, the number of communication rounds in our algorithm is bounded, with high probability, by 78, but the actual number of communication rounds observed so far is 25 in the worst case. Forn⩽10010100 and 4⩽p⩽2048, the number of communication rounds in our algorithm is bounded, with high probability, by 118; and we conjecture that the actual number of communication rounds required will not exceed 50. Our algorithm has a considerably smaller member of communication rounds than the list ranking algorithm used in Reid-Miller’s empirical study of parallel list ranking on the Cray C-90.(1) To our knowledge, Reid-Miller’s algorithm(1) was the fastest list ranking implementation so far. Therefore, we expect that our result will have considerable practical relevance.

We present an algorithm for regular, personalized all- to- all communication, in which every processor has an individual message to deliver to every other processor. Our machine model is a cluster of processing nodes where each node, possibly consisting of several processors, can participate in only one communication operation with another node at a time. The nodes may have different numbers of processors. This general model is important for the implementation of all-to-all communication in libraries such as MPI where collective communication may take place over arbitrary subsets of processors. The algorithm is optimal up to an additive term that is small if the total number of processors is large compared to the maximal number of processors in a node.

We analyze the impact of the structure of the Data Gathering (DG) trees on node lifetime (round of first node failure) and network lifetime (minimum number of rounds by which the network gets either disconnected due to node failures or the fraction of coverage loss reaches a threshold) in wireless sensor networks through extensive simulations. The two categories of DG trees studied are: the Bottleneck Node Weight-Based (BNW-DG) trees and Bottleneck Link Weight-Based (BLW-DG) trees. The BNW-DG trees incur a smaller diameter and a significantly larger fraction of nodes as leaf nodes: thus, protecting a majority of the nodes in the network from simultaneously being exhausted of the energy resources (contributing to a significantly larger network lifetime); nevertheless the nodes that serve as intermediate nodes in the first few instances of the BNW-DG trees are bound to lose their energy more quickly than the other nodes, leading to a smaller node lifetime compared to that of the BLW-DG trees (that incur a larger diameter and a relatively lower fraction of nodes as leaf nodes).

We consider on-line Ramsey numbers defined by a game played between two players, Builder and Painter. In each round Builder draws an the edge and Painter colors it either red or blue, as it appears. Builder's goal is to force Painter to create a monochromatic copy of a fixed graph \(H\) in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly) is the on-line Ramsey number \(\widetilde{r}(H)\) of the graph \(H\). An asymmetric version of the on-line Ramsey numbers \(\widetilde{r}(G,H)\) is defined accordingly. In 2005, Kurek and Rucinski computed \(\widetilde{r}(C_3)\). In this paper, we compute \(\widetilde{r}(C_4,C_k)\) for \(3 \le k \le 7\). Most of the results are based on computer algorithms but we obtain the exact value \(\widetilde{r}(C_4)\) and do so without the help of computer algorithms.

Owing to its practical configuration to edge computing and privacy preservation capabilities, federated learning (FL) has been increasingly appealing in Internet of Things (IoT) networks. However, due to the inherent openness of IoT network architectures, FL clients are susceptible to various attacks, resulting in unreliable local model updates. To address this challenge, federated unlearning (FU) emerges as a viable solution, which can erase such unreliable updates from the FL model using the unlearning operation while preserving model accuracy. Existing FU studies have significant potential, but they are not directly applicable to IoT networks because of their high computational costs and limited capacity to defend against prevalent dynamic attacks in mobile network environments. In this work, we propose FedRemover, a novel FU method specifically tailored for deployment in IoT networks. The key insight behind FedRemover is that model updates will exhibit inconsistency when exposed to attacks. Therefore, we devise a real-time malicious client detection scheme by examining the performance consistency of model updates. Upon detecting malicious clients, FedRemover promptly executes the unlearning operation, achieving an unlearned global model within a minimal number of rounds. This makes FedRemover highly efficient and robust against dynamic attacks, enabling it well-suited for practical deployment in IoT networks. Experiments on three standard datasets demonstrate the efficiency and robustness of FedRemover, with an obvious speed-up of 10× and comparable robustness guarantees compared with benchmark algorithms.

Sublogarithmic approximation for telephone multicast

Dynamical Computing Power Balancing for Adaptive Mesh Refinement Applications

Presents a parallel hash join algorithm that is based on the concept of hierarchical hashing, to address the problem of data skew. The proposed algorithm splits the usual hash phase into a hash phase and an explicit transfer phase, and adds an extra scheduling phase between these two. During the scheduling phase, a heuristic optimization algorithm, using the output of the hash phase, attempts to balance the load across the multiple processors in the subsequent join phase. The algorithm naturally identifies the hash partitions with the largest skew values and splits them as necessary, assigning each of them to an optimal number of processors. Assuming for concreteness a Zipf-like distribution of the values in the join column, a join phase which is CPU-bound, and a shared nothing environment, the algorithm is shown to achieve good join phase load balancing, and to be robust relative to the degree of data skew and the total number of processors. The overall speedup due to this algorithm is compared to some existing parallel hash join methods. The proposed method does considerably better in high skew situations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A parallel hash join algorithm based on the concept of hierarchical hashing is proposed to address the problem data skew. The proposed algorithm adds an extra scheduling phase to the usual hash and join phases. During the scheduling phase, a heuristic optimization algorithm, using the output of the hash phase, attempts to balance the load across the multiple processors in the subsequent join phase. The algorithm naturally identifies the hash partitions with the largest skew elements, splits them up, and assigns each of them to an optimal number of processors. Assuming a Zipf-like distribution of the elements in the join column, the algorithm is shown to achieve good load balancing for the join phase in a CPU-bound environment, and it is shown to be fairly robust relative to the degree of data skew and the total number of processors. The overall speedup due to this algorithm is compared with conventional parallel hash join methods and the considerable advantage of the proposed method is demonstrated even when the additional scheduling phase is taken into account. >

Training set parallelism and network based parallelism are two popular paradigms for parallelizing a feedforward (artificial) neural network. Training set parallelism is particularly suited to feedforward neural networks with backpropagation learning where the size of the training set is large in relation to the size of the network. This paper analyzes training set parallelism for feedforward neural networks when implemented on a transputer array configured in a pipelined ring topology. Theoretical expressions for the time per epoch (iteration) and optimal size of a processor network are derived when the training set is equally distributed among the processing nodes. These show that the speed up is a function of the number of patterns per processor, communication overhead per epoch and the total number of processors in the topology. Further analysis of how to optimally distribute the training set on a given processor network when the number of patterns in the training set is not an integer multiple of the number of processors, is also carried out. It is shown that optimal allocation of patterns in such cases is a mixed integer programming problem. Using this analysis it is found that equal distribution of training patterns among the processors is not the optimal way to allocate the patterns even when the training set is an integer multiple of the number of processors. Extension of the analysis to processor networks comprising processors of different speeds is also carried out. Experimental results from a T805 transputer array are presented to verify all the theoretical results.

In a Distributed Consensus protocol n processors, of which at most t may be faulty, are given initial binary values; after exchanging messages all the processors that are correct must agree on one of the initial values. We measure the quality of a consensus protocol by the following parameters: the total number of processors n, the number of rounds of message exchange r, and the communication complexity, given by the maximal message size.

We study the problem of computing conjunctive queries over large databases on parallel architectures without shared storage. Using the structure of such a query q and the skew in the data, we study tradeoffs between the number of processors, the number of rounds of communication, and the per-processor load —the number of bits each processor can send or can receive in a single round—that are required to compute q . Since each processor must store its received bits, the load is at most the number of bits of storage per processor. When the data are free of skew, we obtain essentially tight upper and lower bounds for one round algorithms, and we show how the bounds degrade when there is skew in the data. In the case of skewed data, we show how to improve the algorithms when approximate degrees of the (necessarily small number of) heavy-hitter elements are available, obtaining essentially optimal algorithms for queries such as skewed simple joins and skewed triangle join queries. For queries that we identify as treelike , we also prove nearly matching upper and lower bounds for multi-round algorithms for a natural class of skew-free databases. One consequence of these latter lower bounds is that for any ε &gt; 0, using p processors to compute the connected components of a graph, or to output the path, if any, between a specified pair of vertices of a graph with m edges and per-processor load that is O ( m / p 1−ε ) requires Ω(log p ) rounds of communication. Our upper bounds are given by simple structured algorithms using MapReduce. Our one-round lower bounds are proved in a very general model, which we call the Massively Parallel Communication (MPC) model, that allows processors to communicate arbitrary bits. Our multi-round lower bounds apply in a restricted version of the MPC model in which processors in subsequent rounds after the first communication round are only allowed to send tuples.