混合线性布局：复杂性、启发式和实验
Mixed Linear Layouts: Complexity, Heuristics, and Experiments
摘要：
图$G = (V,E)$的$k$ -页线性图布局沿着线$\ell$绘制所有顶点，并且在被称为页的$k$不相交半平面之一中绘制每条边，所述页由$\ell$界定。我们考虑两种类型的页面。在堆栈页面中，没有两个边缘应该交叉，在队列页面中，没有边缘应该被另一个边缘嵌套。堆栈（队列）页面中的交叉（嵌套）称为冲突。算法问题是双重的，并且需要计算（i）顶点排序和（ii）边缘的页面分配，使得所得到的布局是无冲突的或冲突最小的。虽然只有堆栈或只有队列页面的线性布局已经得到了很好的研究，但$s,q \ge 1$的混合$s$ -堆栈$q$ -队列布局受到的关注较少。我们展示了NP-完全性结果的识别问题的某些混合线性布局，并提出了一个新的启发式冲突最小化。在一个计算实验的情况下$s, q = 1$，我们表明，新的启发式是一个改进的线性布局比以前的启发式。
英文摘要：
A $k$-page linear graph layout of a graph $G = (V,E)$ draws all vertices along a line $\ell$ and each edge in one of $k$ disjoint halfplanes called pages, which are bounded by $\ell$. We consider two types of pages. In a stack page no two edges should cross and in a queue page no edge should be nested by another edge. A crossing (nesting) in a stack (queue) page is called a conflict. The algorithmic problem is twofold and requires to compute (i) a vertex ordering and (ii) a page assignment of the edges such that the resulting layout is either conflict-free or conflict-minimal. While linear layouts with only stack or only queue pages are well-studied, mixed $s$-stack $q$-queue layouts for $s,q \ge 1$ have received less attention. We show NP-completeness results on the recognition problem of certain mixed linear layouts and present a new heuristic for minimizing conflicts. In a computational experiment for the case $s, q = 1$ we show that the new heuristic is an improvement over previous heuristics for linear layouts.
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