最小支配集问题及其它问题的分布式算法
On distributed algorithms for minimum dominating set problem and beyond
摘要：
本文研究了在实际应用中有广泛应用的最小支配集（MDS）问题和最小全支配集（MTDS）问题。提出了一种计算近似MDS和MTDS的新思想。其次，我们给出了图的MDS的大小的一个上界。我们还提出了一个分布式的随机算法，产生一个（总）支配子集的一个给定的图，其预期的大小等于上界。接下来，我们给出了快速分布式算法计算近似解的MDS和MTDS问题，使用我们的理论结果。MDS问题出现在不同的领域，例如在社交网络，无线网络，机器人等，最常见的是，我们需要计算MDS在一个分布式或并行模型。因此，我们实现了我们的算法在大规模的网络，并比较我们的结果与最先进的算法，以显示我们提出的算法在实践中的效率。我们还展示了如何扩展我们的想法，提出解决$k$ -支配集问题和集合覆盖问题的算法。我们的算法也可以处理的情况下，网络是动态的，或者在这种情况下，我们有限制，在选择MDS的元素。
英文摘要：
In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an upper bound on the size of MDS of a graph. We also present a distributed randomized algorithm that produces a (total) dominating subset of a given graph whose expected size equals the upper bound. Next, we give fast distributed algorithms for computing approximated solutions for the MDS and MTDS problems using our theoretical results. The MDS problem arises in diverse areas, for example in social networks, wireless networks, robotics, and etc. Most often, we need to compute MDS in a distributed or parallel model. So we implement our algorithm on massive networks and compare our results with the state of the art algorithms to show the efficiency of our proposed algorithms in practice. We also show how to extend our idea to propose algorithms for solving $k$-dominating set problem and set cover problem. Our algorithms can also handle the case where the network is dynamic or in the case where we have constraints in choosing the elements of MDS.
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