论文标题
图形燃烧更快的启发式方法
Faster Heuristics for Graph Burning
论文作者
论文摘要
图形燃烧是一个通过离散步骤通过代理通过网络传播的信息的过程。问题是要找到一个必须提供信息的节点的最佳序列,以使网络以最少数量的步骤覆盖。图形燃烧问题是NP-硬化,在文献中提出了两种近似算法和一些启发式方法。在这项工作中,我们提出了三种启发式方法,即基于骨干的贪婪启发式(BBGH),改善了切割角启发式启发式(ICCH)和基于组件的递归启发式启发式(CBRH)。这些主要基于特征向量的中心度度量。 BBGH找到了网络的骨干,并从骨干的顶点挑剔了顶点。 ICCH是最短的启发式路径,并选择顶点从最佳的中央节点中贪婪地燃烧。断开图上的刻录数问题比连接的图上的刻录数要困难。例如,在一条在不相交路径上是np-hard的路径上,燃烧数字问题很容易。实际上,大型网络通常是断开连接的,而且即使连接了输入图,在燃烧过程中,未命中的顶点之间的图可能会被断开。对于断开的图,组件的排序至关重要。我们的CBRH在断开的图表上效果很好,因为它优先考虑组件。所有启发式方法均已在几个台式网络上实施和测试,包括大小超过$ 50 $ k节点的大型网络。该实验还包括与近似算法的比较。我们算法的优点是,它们实施要简单得多,并且比文献中提出的启发式方法更快。
Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes which have to be given information so that the network is covered in least number of steps. Graph burning problem is NP-Hard for which two approximation algorithms and a few heuristics have been proposed in the literature. In this work, we propose three heuristics, namely, Backbone Based Greedy Heuristic (BBGH), Improved Cutting Corners Heuristic (ICCH) and Component Based Recursive Heuristic (CBRH). These are mainly based on Eigenvector centrality measure. BBGH finds a backbone of the network and picks vertex to be burned greedily from the vertices of the backbone. ICCH is a shortest path based heuristic and picks vertex to burn greedily from best central nodes. The burning number problem on disconnected graphs is harder than on the connected graphs. For example, burning number problem is easy on a path where as it is NP-Hard on disjoint paths. In practice, large networks are generally disconnected and moreover even if the input graph is connected, during the burning process the graph among the unburned vertices may be disconnected. For disconnected graphs, ordering of the components is crucial. Our CBRH works well on disconnected graphs as it prioritizes the components. All the heuristics have been implemented and tested on several bench-mark networks including large networks of size more than $50$K nodes. The experimentation also includes comparison to the approximation algorithms. The advantages of our algorithms are that they are much simpler to implement and also several orders faster than the heuristics proposed in the literature.