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Distributed Computations in Next Generation Networks

Salehkaleybar, Saber | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 48186 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Golestani, Jamaloddin
  7. Abstract:
  8. There has been a sudden emergence of next generation networks in the past decade where the primary purposes are data ggregation/mining, distributed information and signal processing, and environmental control and monitoring. The distributed algorithms operating in such networks, should have simple structure and be robust against node failures or network dynamics.Extensive studies on designing and analyzing these algorithms have resulted in introducing different models of distributed systems with similar properties such as gossip algorithms, population protocols, and cellular automata-based systems. In this dissertation, we take first steps toward understanding the computational power of these distributed systems in computing functions. One of the long-standing open problems in this field is the the problem of distributed majority voting. Consider a network with n nodes, where each node initially votes for one (or more) choices out of a set of possible choices. The goal is to design a distributed voting automaton to determine either the choice with maximum vote (the voting problem) or to rank all the choices in terms of their acquired votes (the ranking problem). One of the main questions is whether voting automata exist for any number of multiple choices? Furthermore, what is the minimum number of states of a possible solution? We present a distributed algorithm to solve the voting and ranking problems. The algorithm consolidates node votes across the network by updating the states of interacting nodes using two key operations; the union and the intersection. The proposed algorithm is simple, independent from network size, and easily scalable in terms of the number of choices. We prove the number of states to be optimal in the ranking case; this optimality is conjectured to also apply to the voting case. The time complexity of the algorithm is analyzed in complete graphs. We show that the time complexity for both ranking and voting is inversely proportional to the minimum of the vote percentage differences among various choices.In the more general setting, we consider the problem of distributed function computation where each node has an initial value and the goal is to compute a function of these values in a distributed manner. We propose a novel token-based approach to compute a wide class of target functions. In this approach, node values are attached to tokens and travel across the network. Each pair of travelling tokens would coalesce when they meet, forming a token with a new value as a function of the original token values. In contrast to completely randomized solution, where token movement is governed by random walk, meeting of tokens in our scheme is accelerated by adopting a novel chasing mechanism. We proved that the proposed algorithm results in a significant reduction of time and message complexities. Robustness of the CRW and TCM algorithms in the presence of node failure is analyzed. We show that their robustness can be improved by running multiple instances of the algorithms in parallel.One of the main challenges in the majority voting problem is the robustness of distributed system against failures or malicious attacks. We formulate this problem as a hypothesis testing and propose fixed-size and sequential solutions using classical and Bayesian approaches based on properties of the exponential distribution. The sequential version of the proposed algorithm enables nodes to test which choice is in majority, successively in time. Hence, termination of the algorithm is embedded within it, contrary to the existing approaches which require a monitoring algorithm to indicate the termination. This property renders the algorithm much more efficient in terms of message complexity. Furthermore, we show that the proposed solution is resilient to Byzantine attacks if there exists a path of normal nodes between any two normal nodes
  9. Keywords:
  10. Cellular Automata ; Distributed Computing ; Robustness Evaluation ; Gossip Based Protocol ; Distributed Voting ; Population Protocols ; Distributed Pagerank

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