论文标题
部分可观测时空混沌系统的无模型预测
Recognizing Geometric Intersection Graphs Stabbed by a Line
论文作者
论文摘要
在本文中，我们确定了识别两个图类别的计算复杂性，即\ emph {接地l} - 图和\ emph {stabbable {stabbable网格相交}图。通过将垂直（$ \ vert $）段的底部端点加入水平（$ - $）段的左端点来制作L形。垂直段的顶点被称为L形的{\ em Anchor}。接地的L图是L形的相交图，因此所有L形锚的锚位于同一水平线上。我们表明，识别接地的L-Gaphs是NP完整的。这回答了jel {\'i} nek \＆t {Ö} pfer（Electron。J.Comb。，2019）提出的一个开放问题。 网格相交图是轴 - 并行线段的相交图，其中两个垂直（类似地，两个水平）段无法相交。我们说，如果$ s $相交$ \ ell $，则（不一定是轴 - 平行）$ \ ell $ abt段$ s $。图形$ g $是可刺的网格相交图（$ stabgig $），如果有$ g $的网格交点表示，其中相同的线刺伤其所有细分市场。我们表明，即使在限制的图表上，识别$ stabgig $ graphs也是$ np $ complete。这回答了Chaplick \ etal（\ textsc {o} rder，2018年）提出的一个公开问题。
In this paper, we determine the computational complexity of recognizing two graph classes, \emph{grounded L}-graphs and \emph{stabbable grid intersection} graphs. An L-shape is made by joining the bottom end-point of a vertical ($\vert$) segment to the left end-point of a horizontal ($-$) segment. The top end-point of the vertical segment is known as the {\em anchor} of the L-shape. Grounded L-graphs are the intersection graphs of L-shapes such that all the L-shapes' anchors lie on the same horizontal line. We show that recognizing grounded L-graphs is NP-complete. This answers an open question asked by Jel{\'ı}nek \& T{ö}pfer (Electron. J. Comb., 2019). Grid intersection graphs are the intersection graphs of axis-parallel line segments in which two vertical (similarly, two horizontal) segments cannot intersect. We say that a (not necessarily axis-parallel) straight line $\ell$ stabs a segment $s$, if $s$ intersects $\ell$. A graph $G$ is a stabbable grid intersection graph ($StabGIG$) if there is a grid intersection representation of $G$ in which the same line stabs all its segments. We show that recognizing $StabGIG$ graphs is $NP$-complete, even on a restricted class of graphs. This answers an open question asked by Chaplick \etal (\textsc{O}rder, 2018).
