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ISAAC
2009
Springer

Untangled Monotonic Chains and Adaptive Range Search

9 years 9 months ago
Untangled Monotonic Chains and Adaptive Range Search
Abstract. We present the first adaptive data structure for two-dimensional orthogonal range search. Our data structure is adaptive in the sense that it gives improved search performance for data with more inherent sortedness. Given n points on the plane, the linear-space data structure can answer range queries in O(log n+k+m) time, where m is the number of points in the output and k is the minimum number of monotonic chains into which the point set can be decomposed, which is O( √ n) in the worst case. Our result matches the worst-case performance of other optimaltime linear-space data structures, or surpasses them when k = o( √ n). Our data structure can also be made implicit, requiring no extra space beyond that of the data points themselves, in which case the query time becomes O(k log n + m). We present a novel algorithm of independent interest to decompose a point set into a minimum number of untangled, same-direction monotonic chains in O(kn + n log n) time.
Diego Arroyuelo, Francisco Claude, Reza Dorrigiv,
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where ISAAC
Authors Diego Arroyuelo, Francisco Claude, Reza Dorrigiv, Stephane Durocher, Meng He, Alejandro López-Ortiz, J. Ian Munro, Patrick K. Nicholson, Alejandro Salinger, Matthew Skala
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