Graph problems in call models and switching networks
Author(s)
Advisor
Date
2018-08Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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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 GraphsPolya’s Counting Theorem
Cycle İndex Polynomial
Switching Networks
Call Models