Computing a rectilinear shortest path amid splinegons in plane

Tameem Choudhury; R. Inkulu

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arXiv · 1711.11524

Computing a rectilinear shortest path amid splinegons in plane

Tameem Choudhury·R. Inkulu

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Abstract

We reduce the problem of computing a rectilinear shortest path between two given points s and t in the splinegonal domain \calS to the problem of computing a rectilinear shortest path between two points in the polygonal domain. As part of this, we define a polygonal domain \calP from \calS and transform a rectilinear shortest path computed in \calP to a path between s and t amid splinegon obstacles in \calS. When \calS comprises of h pairwise disjoint splinegons with a total of n vertices, excluding the time to compute a rectilinear shortest path amid polygons in \calP, our reduction algorithm takes O(n + h \lg{n}) time. For the special case of \calS comprising of concave-in splinegons, we have devised another algorithm in which the reduction procedure does not rely on the structures used in the algorithm to compute a rectilinear shortest path in polygonal domain. As part of these, we have characterized few of the properties of rectilinear shortest paths amid splinegons which could be of independent interest.

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Tameem Choudhury, R. Inkulu. 2017-11-30. Computing a rectilinear shortest path amid splinegons in plane. https://arxiv.org/abs/1711.11524

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