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Computing a Rectilinear Shortest Path amid Splinegons in Plane

  • Tameem Choudhury
  • R. Inkulu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)

Abstract

We reduce the problem of computing a rectilinear shortest path between two given points s and t in the given splinegonal domain \(\mathcal {S}\) to the problem of computing a rectilinear shortest path between two points in the polygonal domain. Our reduction algorithm defines a polygonal domain \(\mathcal {P}\) from \(\mathcal {S}\) by identifying a coreset of points on the boundaries of splinegons in \(\mathcal {S}\). Further, it transforms a shortest path between s and t amid polygonal obstacles in \(\mathcal {P}\) to a shortest path between s and t amid splinegonal obstacles in \(\mathcal {S}\). When \(\mathcal {S}\) is comprised of h pairwise disjoint splinegons defined with a total of n vertices, excluding the time to compute a rectilinear shortest path amid polygons in \(\mathcal {P}\), our reduction algorithm takes \(O(n + h \lg {n} + (\lg {h})^{1+\epsilon })\) time. Here, \(\epsilon \) is a small positive constant (resulting from the triangulation of the free space using [2]). For the special case of \(\mathcal {S}\) comprising concave-in splinegons, we have devised another reduction algorithm which does not rely on the structures used in the algorithm (Inkulu and Kapoor [14]) to compute a rectilinear shortest path in the polygonal domain. Further, we have characterized few of the properties of rectilinear shortest paths amid splinegons which could be of independent interest.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIIT GuwahatiGuwahatiIndia

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