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**11 - 12**of**12**### In-Network Leader Selection for Acyclic Graphs

"... Abstract—We study the problem of leader selection in leader-follower multi-agent systems that are subject to stochastic dis-turbances. This problem arises in applications such as vehicle formation control, distributed clock synchronization, and dis-tributed localization in sensor networks. We pose a ..."

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Abstract—We study the problem of leader selection in leader-follower multi-agent systems that are subject to stochastic dis-turbances. This problem arises in applications such as vehicle formation control, distributed clock synchronization, and dis-tributed localization in sensor networks. We pose a new leader selection problem called the in-network leader selection problem. Initially, an arbitrary node is selected to be a leader, and in all consequent steps the network must have exactly one leader. The agents must collaborate to find the leader that minimizes the variance of the deviation from the desired trajectory, and they must do so within the network using only communication between neighbors. To develop a solution for this problem, we first show a connection between the leader selection problem and a class of discrete facility location problems. We then leverage a previously proposed self-stabilizing facility location algorithm to develop a self-stabilizing in-network leader selection algorithm for acyclic graphs. I.

### Information Centrality and Ordering of Nodes for Accuracy in Noisy Decision-Making Networks

- ACCEPTED IN THE IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2015

"... This paper considers a network of stochastic evidence accumulators, each represented by a drift-diffusion model accruing evidence towards a decision in continuous time by observing a noisy signal and by exchanging information with other units according to a fixed communication graph. These network ..."

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This paper considers a network of stochastic evidence accumulators, each represented by a drift-diffusion model accruing evidence towards a decision in continuous time by observing a noisy signal and by exchanging information with other units according to a fixed communication graph. These network dynamics model distributed sequential hypothesis testing as well as collective decision making. We prove the relationship between the location of each unit in the graph and its certainty as measured by the inverse of the variance of its state. Under mild connectivity assumptions, we show that only in balanced directed graphs do the node variances remain within a bounded constant from the minimum possible variance. We then prove that, for these digraphs, node ranking based on certainty is governed by information centrality, which depends on the notion of effective resistance suitably generalized to directed graphs. Our results, which describe the certainty of each unit as a function of the structural properties of the graph, can guide the selection of leaders in problems that involve the observation of noisy external signals by a cooperative multi-agent network.