Dynamic Orthogonal Range Searching on the RAM, Revisited
نویسندگان
چکیده
We study a longstanding problem in computational geometry: 2-d dynamic orthogonal range reporting. We present a new data structure achieving O ( logn log logn + k ) optimal query time and O ( log2/3+o(1) n ) update time (amortized) in the word RAM model, where n is the number of data points and k is the output size. This is the first improvement in over 10 years of Mortensen’s previous result [SIAM J. Comput., 2006], which has O ( log7/8+ε n ) update time for an arbitrarily small constant ε. In the case of 3-sided queries, our update time reduces to O ( log1/2+ε n ) , improving Wilkinson’s previous bound [ESA 2014] of O ( log2/3+ε n ) . 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
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