Point-Location in The Arrangement of Curves
An arrangement of $n$ curves in the plane is given. The query is a point $q$ and the goal is to find the face of the arrangement that contains $q$. A data-structure for point-location, preprocesses the curves into a data structure of polynomial size in $n$, such that the queries can be answered in t...
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| creator | Aghamolaei, Sepideh Ghodsi, Mohammad |
| description | An arrangement of $n$ curves in the plane is given. The query is a point $q$
and the goal is to find the face of the arrangement that contains $q$. A
data-structure for point-location, preprocesses the curves into a data
structure of polynomial size in $n$, such that the queries can be answered in
time polylogarithmic in $n$.
We design a data structure for solving the point location problem queries in
$O(\log C(n)+\log S(n))$ time using $O(T(n)+S(n)\log(S(n)))$ preprocessing
time, if a polygonal subdivision of total size $S(n)$, with cell complexity at
most $C(n)$ can be computed in time $T(n)$, such that the order of the parts of
the curves inside each cell has a monotone order with respect to at least one
segment of the boundary of the cell. We call such a partitioning a
curve-monotone polygonal subdivision. |
| doi_str_mv | 10.48550/arxiv.2007.11451 |
| format | Article |
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and the goal is to find the face of the arrangement that contains $q$. A
data-structure for point-location, preprocesses the curves into a data
structure of polynomial size in $n$, such that the queries can be answered in
time polylogarithmic in $n$.
We design a data structure for solving the point location problem queries in
$O(\log C(n)+\log S(n))$ time using $O(T(n)+S(n)\log(S(n)))$ preprocessing
time, if a polygonal subdivision of total size $S(n)$, with cell complexity at
most $C(n)$ can be computed in time $T(n)$, such that the order of the parts of
the curves inside each cell has a monotone order with respect to at least one
segment of the boundary of the cell. We call such a partitioning a
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and the goal is to find the face of the arrangement that contains $q$. A
data-structure for point-location, preprocesses the curves into a data
structure of polynomial size in $n$, such that the queries can be answered in
time polylogarithmic in $n$.
We design a data structure for solving the point location problem queries in
$O(\log C(n)+\log S(n))$ time using $O(T(n)+S(n)\log(S(n)))$ preprocessing
time, if a polygonal subdivision of total size $S(n)$, with cell complexity at
most $C(n)$ can be computed in time $T(n)$, such that the order of the parts of
the curves inside each cell has a monotone order with respect to at least one
segment of the boundary of the cell. We call such a partitioning a
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and the goal is to find the face of the arrangement that contains $q$. A
data-structure for point-location, preprocesses the curves into a data
structure of polynomial size in $n$, such that the queries can be answered in
time polylogarithmic in $n$.
We design a data structure for solving the point location problem queries in
$O(\log C(n)+\log S(n))$ time using $O(T(n)+S(n)\log(S(n)))$ preprocessing
time, if a polygonal subdivision of total size $S(n)$, with cell complexity at
most $C(n)$ can be computed in time $T(n)$, such that the order of the parts of
the curves inside each cell has a monotone order with respect to at least one
segment of the boundary of the cell. We call such a partitioning a
curve-monotone polygonal subdivision.</abstract><doi>10.48550/arxiv.2007.11451</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Geometry |
| title | Point-Location in The Arrangement of Curves |
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