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arXiv · 1504.06842

An Optimal Algorithm for Minimum-Link Rectilinear Paths in Triangulated Rectilinear Domains

Joseph S. B. Mitchell·Valentin Polishchuk·Mikko Sysikaski·Haitao Wang
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Abstract

We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set $\mathcal{P}$ of $h$ pairwise-disjoint rectilinear polygonal obstacles with a total of $n$ vertices in the plane, a minimum-link rectilinear path between two points is a rectilinear path that avoids all obstacles with the minimum number of edges. In this paper, we present a new algorithm for finding minimum-link rectilinear paths among $\mathcal{P}$. After the plane is triangulated, with respect to any source point $s$, our algorithm builds an $O(n)$-size data structure in $O(n+h\log h)$ time, such that given any query point $t$, the number of edges of a minimum-link rectilinear path from $s$ to $t$ can be computed in $O(\log n)$ time and the actual path can be output in additional time linear in the number of the edges of the path. The previously best algorithm computes such a data structure in $O(n\log n)$ time.

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Joseph S. B. Mitchell, Valentin Polishchuk, Mikko Sysikaski, Haitao Wang. 2015-04-26. An Optimal Algorithm for Minimum-Link Rectilinear Paths in Triangulated Rectilinear Domains. https://arxiv.org/abs/1504.06842

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