最大简单共享问题的快速近似算法

介绍了一种基于复制结点的消除线路交叉的模型.该模型提出了一个优化问题,就是最小化结点复制的数量.同时提出一个自定义问题——"最大简单共享问题",并证明最小化结点复制的数量与最大共享问题是等价的.证明了最大简单共享问题是NP-hard的,给出了一种简单的贪心算法,并证明该贪心算法的近似度为3.引入一个"最大互斥简单共享问题",该问题是最大简单共享问题的2-近似.将其转化为在一系列图上的完美匹配问题,使该问题可以在多项式时间内得到完美解决.最后,在最大互斥简单共享的基础上,用局部搜索的方法将近似度提高到12/7.

An Efficient Approximation Algorithm for Maximum Simple Sharing Problem

This paper introduces a crossing elimination model based on a node duplication method and the authors want to minimize the number of duplication. It is related with an artificial problem, called the maximum simple sharing problem. First it is proved to be NP-hard, then a simple greedy algorithm which achieves an approximation factor of 3. Next the maximum disjoint simple sharing problem is introduced, which is naturally a 2-approximation of the maximum simple sharing problem, and the paper shows that this problem can be solved optimally by reducing to the perfect matching problem in a series of carefully constructed graphs. At last, the approximation factor is further improved to 12/7 with a local search technique.