Abstract
We present a practical implementation of the first adaptive data structure for orthogonal range queries in 2D [Arroyuelo et al., ISAAC 2009]. The structure is static, requires only linear space for its representation, and can even be made implicit. The running time for a query is \(O(\lg k\lg n + \min(k,m)\lg n + m)\), where k is the number of non-crossing monotonic chains in which we can partition the set of points, and m is the size of the output. The space consumption of our implementation is 2n + o(n) words. The experimental results show that this structure is competitive with the state of the art. We also present an alternative construction algorithm for our structure, which in practice outperforms the original proposal by orders of magnitude.
This work was supported in part by NSERC Canada, the Canada Research Chairs Programme, the Go-Bell and David R. Cheriton Scholarships Program, and an Ontario Graduate Scholarship.
An Erratum for this chapter can be found at http://dx.doi.org/10.1007/978-3-642-16321-0_42
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Claude, F., Munro, J.I., Nicholson, P.K. (2010). Range Queries over Untangled Chains. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_8
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