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Abstract
In this dissertation, we study rooted-phylogenetic networks that can be constructed assuming the molecular clock hypothesis. We characterize distance matrices that admit such networks for 3 and 4 taxa. We design an efficient algorithm for a special class of rooted-phylogenetic networks that detects the existence of a network and constructs it. We also design two algorithms for constructing rooted phylogenetic networks optimizing the least-squares fit. Then, we study un-rooted phylogenetic networks based on the split decomposition theory. We derive an algorithm to construct un-rooted phylogenetic networks optimizing the number of edges. Finally, we study the problem of visualizing phylogenetic networks, by making drawings of clustered layered graphs nicer. We give two linear-time algorithms with different preconditions.
