演化網路（phylogenetic networks）為用於表示「不同生物物種或是不同生物分類之間，含有物種混合事件（reticulation events）的演化歷史關係」的有向無環圖。此論文將探討其中兩種網路:單絞接網路（1-articulated networks）與第一級網路（galled trees, level-1 networks）。和它們的生成樹相比，這些網路只多包含了少量的邊，因此我們把它們稱為類樹狀網路（tree-like netowrks）。

此論文主要探討兩個問題。其一為由表示物種之間演化距離的距離矩陣（distance matrices）重建單絞接網路。令n為物種的數量，我們的主要成果是一個時間複雜度為O(n^2)的演算法。在此演算法所建造的網路中，兩物種間的最短演化路線的長度為距離矩陣中的值。另一個問題為第一級網路的編碼。我們在此提出一個緊實的編碼，並證明我們可直接在最佳時間複雜度下用此編碼解決樹包含問題（tree-containment problems, TCP）。

此論文還包括以下相關題目：(1)單絞接網路的樹包含問題。(2)以距離集合矩陣（set-distance matrices）重建單絞接網路。(3)以距離矩陣重建雙絞接網路（2-articulated networks）。

A phylogenetic network is a directed acyclic graph for representing the evolutionary history between species or taxa involving reticulation events. Here, we focus on two classes of phylogenetic networks: 1-articulated networks and galled trees (level-1 networks). Since these networks contain only a small number of additional edges from their embedded spanning tree, we refer to them as tree-like networks.

Two main problems are discussed in the dissertation: The first one is to reconstruct 1-articulated networks from distance matrices, which represent the evolutionary distance between species. Our main result is a O(n^2) time algorithm, where n is the number of species, for constructing networks where the shortest evolutionary path between any pair of species satisfies the input distance. The other is to encode a level-1 network. For this problem, we propose a compact encoding, and show that the tree containment with galled tree can be solved optimally with our encoding.

Other related problems are also discussed in this dissertation. The problems include the \emph{tree containing problem} (TCP) for 1-articulated networks, reconstructing 1-articulated networks from set-distance matrices, and reconstructing 2-articulated networks from distance matrices.

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