Computing Along Routes via Gossiping

Sch. of Electr. & Comput. Eng., Cornell Univ., Ithaca, NY, USA
IEEE Transactions on Signal Processing (Impact Factor: 2.81). 07/2010; DOI: 10.1109/TSP.2010.2045421
Source: DBLP

ABSTRACT In this paper, we study a class of distributed computing problems where a group of nodes (destinations) is interested in a function of data which are stored by another group of nodes (sources). We assume that the function of interest is separable, i.e., it can be decomposed as a sum of functions of local variables, a case that subsumes several interesting types of queries. One approach to solve this problem is to route raw information from the sources to the interested destinations by either unicasting or multicasting. The second approach is to compute the function of interest along some routes while propagating the information from the sources to the destinations. Considering the second scenario, the goal of this paper is to examine how information should be forwarded to the intended recipients, computing along the routes by gossiping with selected neighbors. Unlike efficient unicasting/multicasting problems, nodes are interested in a specific function of the data, rather than the raw data themselves. Moreover, unlike standard gossiping problems, in our case, the information needs to flow in a specific direction. Given the underlying network connectivity and the source-destination sets, we provide necessary and sufficient conditions on the update weights (referred to as codes) so that the destination nodes converge to the desired function of the source values. We show that the evolution of the source states does not affect the feasibility of the problem, and we provide a detailed analysis on the spectral properties of the feasible codes. We also study the problem feasibility under some specific topologies and provide guidelines to determine infeasibility. We also formulate different strategies to design codes, and compare the performance of our solution with existing alternatives.

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    ABSTRACT: In this paper we consider the problem of gossiping in a network to diffuse the average of a sub-set of nodes, called sources, and directing it to another sub-set of nodes in the network called destinations. This case generalizes the typical average consensus gossiping policy, where all nodes are both sources and destinations. We first describe prior results we obtained on a static network topology and gossip policy, high-lighting what conditions lead to the desired information flow. We show that, through semi-directed flows, this formulation allows to solve the problem with lower complexity than using plain gossiping policies. Inspired by these results, we move on to design algorithms to solve the problem in the dynamic case. For the dynamic network scenario we derive conditions under which the network converges to the desired result in the limit. We also provide policies that trade-off accuracy with increased mixing speed for the dynamic asymmetric diffusion problem.
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    ABSTRACT: In this paper, we are studying a class of distributed data aggregation problems where a set of nodes in a network is interested in a function of data that is stored in another set of nodes. Assuming the function of interest is separable, we propose an algorithm based on gossiping schemes. Gossiping protocols are iterative methods based on near neighbor communications, and they are known to be efficient and robust to link/node failures. In this work, after formulating the problem mathematically, and introducing previously proposed necessary and sufficient conditions on the gossiping updates, we introduce several necessary conditions on the feasible codes which will provide significant intuition in determining the (in)feasibility of a given problem. By focusing on stochastic codes, we provide a necessary condition based on topology and discuss scenarios where the codes we seek cannot be found.
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