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      • Bilkent Theses
      • Theses - Department of Computer Engineering
      • Dept. of Computer Engineering - Ph.D. / Sc.D.
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      Graph problems in call models and switching networks

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      Author(s)
      Atmaca, Abdullah
      Advisor
      Aykanat, Cevdet
      Date
      2018-08
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      In the first part of this dissertation, we focus on graph problems that arise in call models. Such models are used to study the combinatorial properties of certain types of calls that include unicast, multicast, and bicast interconnections. Here we focus on bicast calls, and provide closed-form expressions for the number of unlabeled bicast calls when either the number of callers or number of receivers is fixed to 2 or 3. We then obtain lower and upper bounds on the number of such calls by solving an open problem in graph theory, namely counting the number of unlabeled bipartite graphs. Next, these results are extended to left (right) set labeled and set labeled bipartite graphs. In the second part of the dissertation, we focus on wiring and routing problems for one-sided, binary tree switching networks. Specifically, we reduce the O(n) time complexity of the routing algorithm for the one-sided, binary tree switching networks to O(lg n). We also present a new wiring algorithm for one-sided, binary tree switching networks. Finally, an algorithm is presented to locate the cluster in which the terminals of the corresponding one-sided binary tree switching network are paired. The time complexity of this algorithm is shown to be O(lg n).
      Keywords
      Bipartite Graphs
      Polya’s Counting Theorem
      Cycle İndex Polynomial
      Switching Networks
      Call Models
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      http://hdl.handle.net/11693/47752
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      • Dept. of Computer Engineering - Ph.D. / Sc.D. 75
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