Parameterized Algorithms for Book Embedding Problems
Parameterized Algorithms for Book Embedding Problems
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书籍嵌入问题的参数化算法
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
M. Nöllenburg
中科院分区：
文献类型：
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作者：
S. Bhore;R. Ganian;Fabrizio Montecchiani;M. Nöllenburg
图 G 的 k 页书嵌入将 G 的顶点绘制在一条线上，并在以该线为界的 k 个半平面（称为页面）上绘制边，使得同一页面上没有两条边交叉。我们研究确定 G 是否承认 k 页书嵌入的问题，当顶点的线性顺序固定（称为固定顺序书厚度）或不固定（称为书厚度）时。一般来说，这两个问题都是 NP 完全问题。我们证明，固定订单书厚度和书厚度是由图的顶点覆盖数参数化的固定参数易处理的参数，并且固定订单书厚度是由顶点顺序的路径宽度参数化的固定参数易处理的参数。
A k-page book embedding of a graph G draws the vertices of G on a line and the edges on k half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether G admits a k-page book embedding both when the linear order of the vertices is fixed, called Fixed-Order Book Thickness, or not fixed, called Book Thickness. Both problems are known to be NP-complete in general. We show that Fixed-Order Book Thickness and Book Thickness are fixed-parameter tractable parameterized by the vertex cover number of the graph and that Fixed-Order Book Thickness is fixed-parameter tractable parameterized by the pathwidth of the vertex order.