论文标题
在几何图上图形燃烧的NP完整性结果
NP-Completeness Results for Graph Burning on Geometric Graphs
论文作者
论文摘要
图形燃烧在离散的时间步骤上运行。目的是在最少的时间步骤中燃烧给定图中的所有顶点。该数字已知是图的燃烧数。可以使用图形燃烧对社会影响力，警报或社会传染的传播进行建模。燃烧数量越少，差距越快。 一般图的最佳燃烧是NP-HARD。有一个3个附属算法来燃烧一般图，其中许多子类别都有更好的近似因素。在这里，我们研究网格的燃烧；为燃烧的任意网格和燃烧正方形网格的2-及2个拟合算法提供下限。另一方面，燃烧的路径森林，蜘蛛图和最高程度的树木已经众所周知NP完整。在本文中，我们显示了在连接的间隔图，置换图和其他几种几何图类别上作为推论的燃烧问题。
Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number is known to be the burning number of the graph. The spread of social influence, an alarm, or a social contagion can be modeled using graph burning. The less the burning number, the faster the spread. Optimal burning of general graphs is NP-Hard. There is a 3-approximation algorithm to burn general graphs where as better approximation factors are there for many sub classes. Here we study burning of grids; provide a lower bound for burning arbitrary grids and a 2-approximation algorithm for burning square grids. On the other hand, burning path forests, spider graphs, and trees with maximum degree three is already known to be NP-Complete. In this article we show burning problem to be NP-Complete on connected interval graphs, permutation graphs and several other geometric graph classes as corollaries.
