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- W3136973875 abstract "A rectilinear Steiner tree for a set $P$ of points in $mathbb{R}^2$ is a tree that connects the points in $P$ using horizontal and vertical line segments. The goal of Minimal Rectilinear Steiner Tree is to find a rectilinear Steiner tree with minimal total length. We investigate how the complexity of Minimal Rectilinear Steiner Tree for point sets $P$ inside the strip $(-infty,+infty)times [0,delta]$ depends on the strip width $delta$. We obtain two main results. 1) We present an algorithm with running time $n^{O(sqrt{delta})}$ for sparse point sets, that is, point sets where each $1timesdelta$ rectangle inside the strip contains $O(1)$ points. 2) For random point sets, where the points are chosen randomly inside a rectangle of height $delta$ and expected width $n$, we present an algorithm that is fixed-parameter tractable with respect to $delta$ and linear in $n$. It has an expected running time of $2^{O(delta sqrt{delta})} n$." @default.
- W3136973875 created "2021-03-29" @default.
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- W3136973875 date "2021-03-15" @default.
- W3136973875 modified "2023-09-27" @default.
- W3136973875 title "Rectilinear Steiner Trees in Narrow Strips" @default.
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