cs.CG

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# Title:$L_1$ Shortest Path Queries in Simple Polygons

Abstract: Let $P$ be a simple polygon of $n$ vertices. We consider two-point $L_1$ shortest path queries in $P$. We build a data structure of $O(n)$ size in $O(n)$ time such that given any two query points $s$ and $t$, the length of an $L_1$ shortest path from $s$ to $t$ in $P$ can be computed in $O(\log n)$ time, or in $O(1)$ time if both $s$ and $t$ are vertices of $P$, and an actual shortest path can be output in additional linear time in the number of edges of the path. To achieve the result, we propose a mountain decomposition of simple polygons, which may be interesting in its own right. Most importantly, our approach is much simpler than the previous work on this problem.
 Subjects: Computational Geometry (cs.CG); Data Structures and Algorithms (cs.DS) Cite as: arXiv:1809.07481 [cs.CG] (or arXiv:1809.07481v1 [cs.CG] for this version)

## Submission history

From: Haitao Wang [view email]
[v1] Thu, 20 Sep 2018 05:28:56 UTC (268 KB)
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