Solving Minimum Connected Dominating Set on Proper Interval Graph

Jinqin Tian, Hongsheng Ding
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Abstract

To solve connected dominating problem, it is necessary to find minimum connected dominating set (MCDS for short). However, to find MCDS is NP-hardness. So, a model of graphs called interval graph was constructed from nodes of related network. Two greedy algorithms with linear (or polynomial time) were used to find MCDS on proper interval graph (or interval graph), and have 1 approximation ratio on the graphs. And spanning trees were constructed and used to validate the correctness and effectiveness of corresponding algorithms.
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固有区间图上最小连通支配集的求解
为了解决连通控制问题,需要找到最小连通控制集(简称MCDS)。而MCDS的求法是np -硬度。因此,从相关网络的节点出发,构造了一种称为区间图的图模型。采用线性(或多项式)贪心算法在适当区间图(或区间图)上寻找MCDS,并且在图上具有1个近似比。并构造了生成树来验证相应算法的正确性和有效性。
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