Tahbaz Salehi, Alireza

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Now showing 1 - 4 of 4
  • Publication
    Complex Networks: New Models and Distributed Algorithms
    (2009-12-22) Tahbaz Salehi, Alireza
    Over the past few years, a consensus has emerged among scientists and engineers that net-centric technology can provide unprecedented levels of performance, robustness, and efficiency. Success stories such as the Internet, distributed sensor networks, and multi-agent networks of mobile robots are only a few examples that support this view. The important role played by complex networks has been widely observed in various physical, natural, and social systems. Given the complexity of many of these systems, it is important to understand the fundamental rules that govern them and introduce appropriate models that capture such principles, while abstracting away the redundant details. The main goal of this thesis is to contribute to the emerging field of "network science'' in two ways. The first part of the thesis focuses on the question of information aggregation over complex networks. The problem under study is the asymptotic behavior of agents in a network when they are willing to share information with their neighbors. We start by focusing on conditions under which all agents in the network will asymptotically agree on some quantity of interest, what is known as the consensus problem. We present conditions that guarantee asymptotic agreement when inter-agent communication links change randomly over time. We then propose a distributed (non-Bayesian) algorithm that enables agents to not only agree, but also learn the true underlying state of the world. We prove that our proposed learning rule results in successful information aggregation, in the sense that all agents asymptotically learn the truth as if they were completely informed of all signals and updated their beliefs rationally. Moreover, the simplicity of our local update rule guarantees that agents eventually achieve full learning, while at the same time, avoiding highly complex computations that are essential for full Bayesian learning over networks. The second part of this thesis focuses on presenting a new modeling paradigm that greatly expands the tool set for mathematical modeling of networks, beyond graphs. The approach taken is based on using simplicial complexes, which are objects of study in algebraic topology, as generalizations of graphs to higher dimensions. We show how simplicial complexes serve as more faithful models of the network and are able to capture many of its global topological properties. Furthermore, we develop distributed algorithms for computing various topological invariants of the network. These concepts and algorithms are further explored in the context of a specific application: coverage verification in coordinate-free sensor networks, where sensor nodes have no access to location, distance, or orientation information. We propose real-time, scalable, and decentralized schemes for detection of coverage holes, as well as computation of a minimal set of sensors required to monitor a given region of interest. The presented algorithms clarify the benefits of using simplicial complexes and simplicial homology, instead of applying tools from graph theory, in modeling and analyzing complex networks.
  • Publication
    Distributed coverage verification in sensor networks without location information
    (2008-12-11) Tahbaz-Salehi, Alireza; Jadbabaie, Ali
    In this paper, we present a distributed algorithm for detecting coverage holes in a sensor network with no location information. We demonstrate how, in the absence of localization devices, simplicial complexes and tools from computational homology can be used in providing valuable information on the properties of the cover. In particular, we capture the combinatorial relationships among the sensors by the means of the Rips complex, which is the generalization of the proximity graph of the network to higher dimensions. Our approach is based on computation of a certain generator of the first homology of the Rips complex of the network. We formulate the problem of localizing coverage holes as an optimization problem to compute the sparsest generator of the first homology classes. We also demonstrate how subgradient methods can be used in solving this optimization problem in a distributed manner. Finally, non-trivial simulations are provided that illustrate the performance of our algorithm.
  • Publication
    Distributed Topology Control of Dynamic Networks
    (2008-06-11) Zavlanos, Michael M; Tahbaz-Salehi, Alireza; Jadbabaie, Ali; Pappas, George J
    In this paper, we present a distributed control framework for controlling the topology of dynamic multi-agent networks. Agents are equipped with local sensing and wireless communication capabilities, however, due to power constraints, they are required to switch between two modes of operation, namely active and sleep. The control objective investigated in this paper is to determine distributed coordination protocols that regulate switching between the operation modes of every agent such that the overall network guarantees multi-hop communication links among a subset of so called boundary agents. In the proposed framework, coordination is based on a virtual market where every request to switch off is associated with a bid. Combinations of requests are verified with respect to connectivity and the one corresponding to the highest aggregate bid is finally served. Other than nearest neighbor information, our approach assumes no knowledge of the network topology, while verification of connectivity relies on notions of algebraic graph theory as well as gossip algorithms run over the network. Integration of the individual controllers results in an asynchronous networked control system for which we show that it satisfies the connectivity specification almost surely. We finally illustrate efficiency of our scalable approach in nontrivial computer simulations.
  • Publication
    Distributed coverage verification in sensor networks without location information
    (2008-12-09) Tahbaz-Salehi, Alireza; Jadbabaie, Ali
    In this paper, we present a distributed algorithm for detecting coverage holes in a sensor network with no location information. We demonstrate how, in the absence of localization devices, simplicial complexes and tools from computational homology can be used in providing valuable information on the properties of the cover. In particular, we capture the combinatorial relationships among the sensors by the means of the Rips complex, which is the generalization of the proximity graph of the network to higher dimensions. Our approach is based on computation of a certain generator of the first homology of the Rips complex of the network. We formulate the problem of localizing coverage holes as an optimization problem to compute the sparsest generator of the first homology classes. We also demonstrate how subgradient methods can be used in solving this optimization problem in a distributed manner. Finally, non-trivial simulations are provided that illustrate the performance of our algorithm.