Math @ Duke

Publications [#235431] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Grove, EF; Murali, TM; Vitter, JS, Binary space partitions for fat rectangles,
SIAM Journal on Computing, vol. 29 no. 5
(2000),
pp. 14221448 [doi]
(last updated on 2018/10/19)
Abstract: We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, twodimensional rectangles in R3 such that the aspect ratio of each rectangle in S is at most α, for some constant α≥1. We present an n2O(√log n)time algorithm to build a binary space partition of size n2O(√log n) for S. We also show that if m of the n rectangles in S have aspect ratios greater than α, we can construct a BSP of size n√m2O(√log n) for S in n√m2O(√log n) time. The constants of proportionality in the bigoh terms are linear in log α. We extend these results to cases in which the input contains nonorthogonal or intersecting objects.


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