Fault-Tolerant Aggregation: Flow-Updating Meets Mass-Distribution

Flow-Updating (FU) is a fault-tolerant technique that has proved to be efficient in practice for the distributed computation of aggregate functions in communication networks where individual processors do not have access to global information. Previous distributed aggregation protocols, based on repeated sharing of input values (or mass) among processors, sometimes called Mass-Distribution (MD) protocols, are not resilient to communication failures (or message loss) because such failures yield a loss of mass. In this paper, we present a protocol which we call Mass-Distribution with Flow-Updating (MDFU). We obtain MDFU by applying FU techniques to classic MD. We analyze the convergence time of MDFU showing that stochastic message loss produces low overhead. This is the first convergence proof of an FU-based algorithm. We evaluate MDFU experimentally, comparing it with previous MD and FU protocols, and verifying the behavior predicted by the analysis. Finally, given that MDFU incurs a fixed deviation proportional to the message-loss rate, we adjust the accuracy of MDFU heuristically in a new protocol called MDFU with Linear Prediction (MDFU-LP). The evaluation shows that both MDFU and MDFU-LP behave very well in practice, even under high rates of message loss and even changing the input values dynamically.Comment: 18 pages, 5 figures, To appear in OPODIS 201

Stochastic Trade Networks

This paper develops a simple network model to describe the dynamic of the intensive and extensive margin of international trade flows. The result is achieved by means of the combination of two mechanisms of proportional growth: the first (discrete) determines the formation of trade links, the second (continuous) governs trade intensity. We show that our setup is able to simultaneously match a large number of empirical regularities, such as the fraction of zero trade flows across pairs of countries or the high concentration of trade with respect to both products and destinations. Our findings suggest that stylized facts are strongly interconnected across different levels of aggregation of trade data , so that a unifying explanation is called for. By incorporating stochastic elements into standard trade models we can improve their ability to explain relevant facts about world trade

Frictional Unemployment on Labor Flow Networks

We develop an alternative theory to the aggregate matching function in which workers search for jobs through a network of firms: the labor flow network. The lack of an edge between two companies indicates the impossibility of labor flows between them due to high frictions. In equilibrium, firms' hiring behavior correlates through the network, generating highly disaggregated local unemployment. Hence, aggregation depends on the topology of the network in non-trivial ways. This theory provides new micro-foundations for the Beveridge curve, wage dispersion, and the employer-size premium. We apply our model to employer-employee matched records and find that network topologies with Pareto-distributed connections cause disproportionately large changes on aggregate unemployment under high labor supply elasticity

Entrograms and coarse graining of dynamics on complex networks

Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov process according to a partition impacts on the thus obtained lower-dimensional dynamics. We highlight that for a dynamics on a particular graph there may be multiple coarse grained descriptions that capture different, incomparable features of the original process. For instance, a coarse graining induced by one partition may be commensurate with a time-scale separation in the dynamics, while another coarse graining may correspond to a different lower-dimensional dynamics that preserves the Markov property of the original process. Taking inspiration from the literature of Computational Mechanics, we find that a convenient tool to summarise and visualise such dynamical properties of a coarse grained model (partition) is the entrogram. The entrogram gathers certain information-theoretic measures, which quantify how information flows across time steps. These information theoretic quantities include the entropy rate, as well as a measure for the memory contained in the process, i.e., how well the dynamics can be approximated by a first order Markov process. We use the entrogram to investigate how specific macro-scale connection patterns in the state-space transition graph of the original dynamics result in desirable properties of coarse grained descriptions. We thereby provide a fresh perspective on the interplay between structure and dynamics in networks, and the process of partitioning from an information theoretic perspective. We focus on networks that may be approximated by both a core-periphery or a clustered organization, and highlight that each of these coarse grained descriptions can capture different aspects of a Markov process acting on the network.Comment: 17 pages, 6 figue