为什么某些子图计算只需要线性时间

M. Bern, E. Lawler, A. Wong
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引用次数: 29

摘要

计算图论中的一个一般问题是找到给定加权图g的最优子图H。匹配问题(很容易)和旅行推销员问题(不容易)是这个一般问题的众所周知的例子。在文献中,我们也可以找到各种特殊算法来解决线性时间内的某些特殊情况。我们提出了一种构造线性时间算法的一般方法,在这种情况下,图G是由某些组成规则定义的(如树、序列平行图和外平面图),并且期望的子图H满足“规则”性质(如独立性或匹配)。该方法被应用于获得一个线性时间算法来计算树的冗余数,这是一个以前没有多项式时间算法的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Why certain subgraph computations requite only linear time
A general problem in computational graph theory is that of finding an optimal subgraph H of a given weighted graph G. The matching problem (which is easy) and the traveling salesman problem (which is not) are well known examples of this general problem. In the literature one can also find a variety of ad hoc algorithms for solving certain special cases in linear time. We present a general methodology for constructing linear time algorithms in the case that the graph G is defined by certain rules of composition (as are trees, series parallel graphs, and outerplanar graphs) and the desired subgraph H satisfies a "regular" property (such as independence or matching). This methodology is applied to obtain a linear time algorithm for computing the irredundance number of a tree, a problem for which no polynomial time algorithm was previously known.
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