Abstract
We show that there is always a binary space partition (BSP) of size O(n log k) and an autopartition of size O(nk) for n disjoint line segments in the plane, assuming that the segments have k distinct orientations. In particular, if k is a constant, these bounds imply that there is a linear-size BSP and autopartition. Our proof is constructive and can be turned into algorithms computing such a BSP or autopartition in O(n2 ) and O(n2k ) times.
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