Abstract
We present data structures that can answer window queries for a sequence of geometric objects, such as points, line segments, triangles and convex c-gons. We first present data structures to solve windowed intersection decision problems using line segments, triangles and convex c-gons. We also present data structures to count points on maximal layer, to decide whether a given point belongs to a maximal layer, and to count k-dominant points for a fixed integer k for a sequence of points in \(\mathbb {R}^d\), \(d \ge 2\). All data structures presented in this paper answer queries in polylogarithmic time and use subquadratic space.
This research work was supported by NSERC Research Grants and Ontario Graduate Scholarship.
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Chanchary, F., Maheshwari, A., Smid, M. (2018). Window Queries for Problems on Intersecting Objects and Maximal Points*. In: Panda, B., Goswami, P. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2018. Lecture Notes in Computer Science(), vol 10743. Springer, Cham. https://doi.org/10.1007/978-3-319-74180-2_17
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DOI: https://doi.org/10.1007/978-3-319-74180-2_17
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