Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Optimal parallel algorithms for transitive closure and point location in planar structures
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
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Throughout this paper, we use the term subdivision as a shorthand for “a subdivision of E2 into convex regions”. A subdivision is said to be of size n if it is made of n convex (open) regions, and it is of degree d if every region is adjacent to at most d other regions. We define the line span of a subdivision as the maximum number of regions which can be intersected by a single line (section 3).