Abstract
We present an O(nrG) time algorithm for computing and maintaining a minimum length shortest watchman tour that sees a simple polygon under monotone visibility in direction \(\theta \), while \(\theta \) varies in \([0,180^{\circ })\), obtaining the directions for the tour to be the shortest one over all tours, where n is the number of vertices, r is the number of reflex vertices, and \(G\le r\) is the maximum number of gates of the polygon used at any time in the algorithm.
Bengt J. Nilsson is supported by grant 2018-04001 from the Swedish Research Council, David Orden by H2020-MSCA-RISE project 734922-CONNECT and project MTM2017-83750-P of the Spanish Ministry of Science (AEI/FEDER, UE), Carlos Seara by H2020-MSCA-RISE project 734922-CONNECT, projects MTM2015-63791-R MINECO/FEDER and Gen. Cat. DGR 2017SGR1640, and Paweł Żyliński by grant 2015/17/B/ST6/01887 from the National Science Centre, Poland.
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Nilsson, B.J., Orden, D., Palios, L., Seara, C., Żyliński, P. (2020). Shortest Watchman Tours in Simple Polygons Under Rotated Monotone Visibility. In: Kim, D., Uma, R., Cai, Z., Lee, D. (eds) Computing and Combinatorics. COCOON 2020. Lecture Notes in Computer Science(), vol 12273. Springer, Cham. https://doi.org/10.1007/978-3-030-58150-3_25
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