In 1998 , zhou , xiong and zhu improved sh algorithm by reducing this complexity to 2n - lg n . in this paper , we make further improvement . the overall complexity of computing distances is reduced to 3n - lg n 2 , which is only half that of sh algorithm 但是距離的計算量相對于其他基本代數或者邏輯操作來說開銷比較大,所以如何降低整個算法過程中距離的計算次數成為我們考慮的重點,我們改進的目標就是使得計算距離的復雜度盡可能的小。
In one process of combination , the euclidean distances between 3n pairs of points need to be computed , so the overall complexity of computing distance is then 3n - lg n . since the computation of distance is more costly compared with other basic operation , how to improve sh algorithm from the aspect of complexity of computing distance is considered 對帶左半部分內的每個點,算法需要考慮帶右半部分內的至多6個點,假設平面上點的個數為n ,該算法在歸并時最壞情況下需要求出3n對點對之間的距離,從而整個算法計算距離的復雜度為3n lg n 。