关于一类方形双连环网的算法

双连环网(DLN)作为一种网络结构最初于1974年由D．Coppersmith和C．K．Wong提出．近年来，对DLN的研究日渐广泛．众所周知，DLN的最小距离图形(MDD)是L形的．给定一个正数N，能否找到一个双连环网，使它的直径是所有具有N个结点的DLN中最小的是一个有趣的问题．对于一个L形的图形来说，它的直径很容易计算．基于此，为了寻找到上述的DLN，许多专家进行了不懈的研究，也获得了许多好的结果。在本中，作者提出了一个寻找方形双连环网的O(1)快速算．所用方法仅涉及到初等数论的知识。

On Finding the Degenerate DLN

Double Loop Network (DLN) was introduced by D. Coppersmith and C. K. Wong in 1974 and has been widely studied as architecture for local networks since then. It is well-known that the Minimum Distance Diagram (MDD) of a double loop network yields a L-shape. Given a N, it is desirable to find a double-loop network DL(N;s_1,s_2) with its diameter being the minimum among all double loop networks with N nodes. Since the diameter can be easily computed from a L-shape, one method is to start with a desirable L-shape and then asks whether there exist s_1 and s_2 (also called the steps of the DLN) to realize it. Many excellent efforts have been made to find the steps of DLNs to realize the given L-shape. In particular, the rectangular L-shape (also called the degeneration) has special characteristic as well as applications. In this paper, the author provide an excellent method to find the degeneration with an O(1) algorithm, which beats other analogues. The technique only involves some elementary number theory and is very easy to be implemented.