It is proved that a large class of distributed tasks cannot be solved in the presence of faulty processors. This class contains tasks whose unsolvability in the presence of faults is known as well as some new tasks. I...
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It is proved that a large class of distributed tasks cannot be solved in the presence of faulty processors. This class contains tasks whose unsolvability in the presence of faults is known as well as some new tasks. In particular, the authors introduce the notion of the decision graph of a task, and show that every problem whose decision graph is disconnected cannot be solved in the presence of one faulty processor, by reducing the unsolvability of this problem to the unsolvability of the consensus problem. The notion of unsolvability used here is very weak: one says that a protocol solves a given problem in spite of one faulty processor if in any execution it satisfies (i) all nonfaulty processors eventually halt, and (ii) if no processor is faulty, it solves the problem. Hence, the unsolvability of a problem in this model implies its unsolvability in other models appearing in the literature.
This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own stat...
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This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own states in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. It is shown that a quantized consensus is reached for an arbitrary quantizer by means of the stochastic gossip algorithm proposed in a recent paper. The expected value of the time at which a quantized consensus is reached is lower and upper bounded in terms of the topology of the graph for a uniform quantizer. In particular, it is shown that these bounds are related to the principal submatrices of the weighted Laplacian matrix. A convex optimization is also proposed to determine a set of probabilities used to pick a pair of agents that leads to a fast convergence of the gossip algorithm.
Graphs are found in a plethora of domains, including online social networks, the World Wide Web and the study of epidemics, to name a few. With the advent of greater volumes of information and the need for continuousl...
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Graphs are found in a plethora of domains, including online social networks, the World Wide Web and the study of epidemics, to name a few. With the advent of greater volumes of information and the need for continuously updated results under temporal constraints, it is necessary to explore alternative approaches that further enable performance improvements. In the scope of stream processing over graphs, we research the trade-offs between result accuracy and the speedup of approximate computation techniques. The relationships between the frequency of graph algorithm execution, the update rate and the type of update play an important role in applying these techniques. Herein we present VeilGraph, through which we conducted our research. We showcase an innovative model for approximate graph processing implemented in Apache Flink. We analyse the feasibility of our model and evaluate it with the case study of the PageRank algorithm, the most famous measure of vertex centrality used to rank websites in search engine results. Our experiments show that VeilGraph can often reduce latency closely to half (speedup of 2.0x), while achieving result quality above 95% when compared to results of the traditional version of PageRank executing in Apache Flink with Gelly (i.e. without any summarization or approximation techniques). In some cases, depending on the workload, speedups against Apache Flink reach up to 3.0x (i.e. yielding a reduction of up to 66% in latency). We have found VeilGraph implementation on Flink to be scalable, as it is able to improve performance up to 10X speedups, when more resources are employed (16 workers), achieving better speedups with scale for larger graphs, which are the most relevant.
In this paper, a new algorithm based on hierarchical aggregation/disaggregation and decomposition/composition (HAD) scheme is proposed to solve the optimal routing problems (ORP) for hierarchically structured networks...
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In this paper, a new algorithm based on hierarchical aggregation/disaggregation and decomposition/composition (HAD) scheme is proposed to solve the optimal routing problems (ORP) for hierarchically structured networks of multi-layer backbones. Our algorithm has two major differences with the existing HAD algorithms for hierarchically clustered networks [1], [2]: 1) our algorithm works with more general networks than the networks with the clustered structure;2) our algorithm parallelizes the computations for different commodities (message flows defined by a pair of origin node and destination node) so that it speeds up with a parallel time complexity of O(mlog(2)(n)), which is much less than O(Mlog(2)(n)) needed for the existing HAD algorithms. Here, n is the number of nodes in the network;M is the number of commodities and m is a positive number usually much smaller than M and is a function of the patterns of all the commodities including the locations of all origin nodes and destination nodes, and the flow demand of each commodity. Furthermore, our algorithm can make a trade-off between the run time and the optimality, i.e., by allowing the solution to be sub-optimal, our algorithm can save great amount of computation time. The implementation of the algorithm for a 200-node network is simulated using OPNET simulation package (OPNET or Optimized Network Engineering Tools is developed by MIL3, Inc.), and the test results are consistent with our analysis.
Iterative distributed algorithms are studied for computing arithmetic averages over networks of agents connected through memoryless broadcast erasure channels. These algorithms do not require the agents to have any kn...
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Iterative distributed algorithms are studied for computing arithmetic averages over networks of agents connected through memoryless broadcast erasure channels. These algorithms do not require the agents to have any knowledge about the global network structure or size. Almost sure convergence to state agreement is proved, and the communication and computational complexities of the algorithms are analyzed. Both the number of transmissions and the number of computations performed by each agent of the network are shown to grow not faster than poly-logarithmically in the desired precision. The impact of the graph topology on the algorithms performance is analyzed as well. Moreover, it is shown how, in the presence of noiseless communication feedback, one can modify the algorithms, significantly improving their performance versus complexity trade-off. (C) 2010 Elsevier Ltd. All rights reserved.
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