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Ray-shooting and shortest-path queries take time $O(\\log ^3 n)$ (plus $O(k)$ time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take $O(\\log ^3 n)$ time (amortized for vertex updates). This is the first polylog-time dynamic data structure for shortest-path and ray-shooting queries. It is also the first dynamic point-location data structure for connected planar maps that achieves optimal query time.<\/jats:p>","DOI":"10.1137\/s0097539792224516","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:43:31Z","timestamp":1109227411000},"page":"207-233","source":"Crossref","is-referenced-by-count":19,"title":["A Unified Approach to Dynamic Point Location, Ray shooting, and Shortest Paths in Planar Maps"],"prefix":"10.1137","volume":"25","author":[{"given":"Yi-Jen","family":"Chiang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Franco P.","family":"Preparata","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roberto","family":"Tamassia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02189304"},{"key":"R2","unstructured":"Hanna Baumgarten, Hermann Jung, Kurt Mehlhorn,  Dynamic point location in general subdivisions,  Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms (Orlando, FL, 1992), ACM, New York,  1992,  250\u2013258 1 173 8980829.68119"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0214041"},{"key":"R4","unstructured":"G. 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