论文标题
转弯序列的达到性
Reachability of turn sequences
论文作者
论文摘要
左和右转的转弯序列被实现为一个简单的整体段的直线链，其弯曲的转弯与转弯序列相同。链条从原点开始，并在某个时候结束，我们称之为回合序列的可触点。我们研究了给定转弯序列的一组可触及点的组合和几何特性，例如形状，连接性以及足够和必要的条件，以达到四个签名轴的可及性。我们还证明了从原点到签名轴上最接近到达点的最大距离的上限和下限，以转弯序列。边界是用序列中的左和右弯数之间的差来表示的，在某些情况下，最大单调前缀的长度或转向序列的后缀的长度。对于某些签名的轴，在添加剂常数中，边界完全匹配或紧密。
A turn sequence of left and right turns is realized as a simple rectilinear chain of integral segments whose turns at its bends are the same as the turn sequence. The chain starts from the origin and ends at some point which we call a reachable point of the turn sequence. We investigate the combinatorial and geometric properties of the set of reachable points of a given turn sequence such as the shape, connectedness, and sufficient and necessary conditions on the reachability to the four signed axes. We also prove the upper and lower bounds on the maximum distance from the origin to the closest reachable point on signed axes for a turn sequence. The bounds are expressed in terms of the difference between the number of left and right turns in the sequence as well as, in certain cases, the length of the maximal monotone prefix or suffix of the turn sequence. The bounds are exactly matched or tight within additive constants for some signed axes.
