Abstract
Given a simple polygon P and a segment e of P, we define the terms completely k-visible, strongly k-visible, and weakly k-visible with respect to P. Two points x and y are said to be k-visible when the line segment xy intersects the boundary of the polygon at most k times. If all of P is k-visible to all of e, then P is completely k-visible from e, but if the entirety of P is k-visible from a subset of e, then P is strongly k-visible from e. Conversely, if e can only see all of P through a set of disjoint intervals, then e is weakly visible. We propose two methods to determine whether P is completely, and strongly k-visible. We also develop an algorithm to calculate the weakly k-visible part of P from e in \(O(kn^4)\) time complexity.
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Bahoo, Y., Kundu, S., Manastyrski, K. (2023). Segment Visibility for k-Transmitters. In: Georgiou, K., Kranakis, E. (eds) Algorithmics of Wireless Networks. ALGOWIN 2023. Lecture Notes in Computer Science, vol 14061. Springer, Cham. https://doi.org/10.1007/978-3-031-48882-5_1
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DOI: https://doi.org/10.1007/978-3-031-48882-5_1
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