Abstract
We present a new algorithm for finding minimum-link rectilinear paths among h rectilinear obstacles with a total of n vertices in the plane. After the plane is triangulated, for any 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, we can compute a minimum-link rectilinear path from s to t in \(O(\log n+k)\) time, where k is the number of edges of the path, and the query time is \(O(\log n)\) if we only want to know the value k. The previously best algorithm solves the problem in \(O(n\log n)\) time.
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Acknowledgments
J. Mitchell is partially supported by grants from Sandia National Labs, the National Science Foundation (CCF-1018388), and the US-Israel Binational Science Foundation (award 2010074). V. Polishchuk is supported by grant 2014-03476 from the Sweden’s innovation agency VINNOVA. H. Wang is supported in part by NSF under Grant CCF-1317143.
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Mitchell, J.S.B., Polishchuk, V., Sysikaski, M., Wang, H. (2015). An Optimal Algorithm for Minimum-Link Rectilinear Paths in Triangulated Rectilinear Domains. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_77
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