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- W2094649462 abstract "We show that the combinatorial complexity of a single cell in an arrangement of k convex polyhedra in 3-space having n facets in total is $O(nk^{1+varepsilon})$ , for any $varepsilon > 0$ , thus settling a conjecture of Aronov et al. We then extend our analysis and show that the overall complexity of the zone of a low-degree algebraic surface, or of the boundary of an arbitrary convex set, in an arrangement of k convex polyhedra in 3-space with n facets in total, is also $O(nk^{1+varepsilon})$ , for any $varepsilon > 0$ . Finally, we present a deterministic algorithm that constructs a single cell in an arrangement of this kind, in time $O(nk^{1+varepsilon} log^3{n})$ , for any $varepsilon > 0$ ." @default.
- W2094649462 created "2016-06-24" @default.
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- W2094649462 date "2006-12-12" @default.
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- W2094649462 title "A Single Cell in an Arrangement of Convex Polyhedra in ${Bbb R}^3$" @default.
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- W2094649462 doi "https://doi.org/10.1007/s00454-006-1272-9" @default.
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