## Abstract

A rectilinear Steiner tree for a set K of points in the plane is a tree that connects k using horizontal and vertical lines. In the Rectilinear Steiner Tree problem, the input is a set K={z_{1},z_{2},..., z_{n}} of n points in the Euclidean plane (R^{2}), and the goal is to find a rectilinear Steiner tree for k of smallest possible total length. A rectilinear Steiner arborescence for a set k of points and a root r ∈ K is a rectilinear Steiner tree T for K such that the path in T from r to any point z ∈ K is a shortest path. In the Rectilinear Steiner Arborescence problem, the input is a set K of n points in R^{2}, and a root r ∈ K, and the task is to find a rectilinear Steiner arborescence for K, rooted at r of smallest possible total length. In this article, we design deterministic algorithms for these problems that run in 2^{O}(nlog n) time.

Original language | English |
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Article number | 21 |

Journal | ACM Transactions on Algorithms |

Volume | 16 |

Issue number | 2 |

DOIs | |

State | Published - 1 Apr 2020 |

Externally published | Yes |

## Keywords

- Rectilinear Steiner tree
- rectilinear Steiner arborescence
- subexponential exact algorithm
- treewidth algorithm

## ASJC Scopus subject areas

- Mathematics (miscellaneous)