在一個無向圖中，兩節點之間的傳輸成本為其最短路徑之長度，而對此圖之擴張樹而言，其傳輸成本為兩兩節點在此樹上之傳輸成本之總和。尋找一個低傳輸成本之擴張樹，確實是網路設計上重要的問題。
兩節點之通訊成本定義為其傳輸成本乘上其傳輸需求量，而一擴張樹的通訊成本為兩兩節點在此樹上之通訊成本之和。給定各個節點的權重，其中一個問題係假設兩個節點之傳輸需求量為此兩節點權重之乘積，其目標在尋找最低通訊成本的擴張樹，另一個問題則假設兩點的傳輸需求量為此兩節點之權重之和。

另一個被研究的問題是如何有效利用另外給定的一些額外金錢，改善原本的網路架構，使得改善後的網路架構可以得到較低的傳輸成本。當然其結果可以應用在相關的網路設計問題上。

Given an undirected graph with nonnegative costs on the edges, the routing cost of a pair of vertices is the cost of the shortest path between them, and the routing cost of any of its spanning trees is the sum over all pairs of vertices of the routing cost in the tree. The communication cost of a pair of vertices is its routing cost multiplied by a given requirement, and the communication cost of a spanning tree is the sum over all pairs of vertices of the communication cost in the tree. Finding a spanning tree of minimum routing cost in edge-weighted undirected general graph is known to be NP-hard, and some approximation algorithms are presented. Another problem is how to improve routing cost on any network structures using extra cost. This problem will be discussed in this thesis.

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