Binary space partitions for fat rectangles

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:457678

Agarwal, P K; Murali, T M; Vitter, J S ^[1]; Grove, E F ^[2]

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1. Duke Univ., Durham, NC (United States)
2. Max-Planck-Institut fuer Informatik, Saarruecken (Germany)

We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in R{sup 3} such that the aspect ratio of each rectangle in S is at most {alpha}, for some constant {alpha} {ge} 1. We present an n2{sup O}({radical}log n)-time algorithm to build a binary space partition of size n2{sup O}({radical}log n) for S. We also show that if m of the n rectangles in S have aspect ratios greater than {alpha}, we can construct a BSP of size n{radical}m2{sup O}({radical}log n) for S in n{radical}m2{sup O}({radical}log n) time. The constants of proportionality in the big-oh terms are linear in log {alpha}. We extend these results to cases in which the input contains non-orthogonal or intersecting objects.

• OSTI ID: 457678
• Report Number(s): CONF-961004--; CNN: Grant CCR-93-01259; Grant DAAH04-96-1-0013; Grant DAAH04-93-G-0076; Grant CCR-9522047
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
COMPUTER GRAPHICS
MATHEMATICAL LOGIC
RECTANGULAR CONFIGURATION
SET THEORY