### Abstract

The problem of constructing a spanning tree for a graph G = (V, E) with n vertices whose maximal degree is the smallest among all spanning trees of G is considered. This problem is easily shown to be NP-hard. In the Steiner version of this problem, along with the input graph, a set of distinguished vertices D ⊆ V is given. A minimum-degree Steiner tree is a tree of minimum degree which spans at least the set D. Iterative polynomial time approximation algorithms for the problems are given. The algorithms compute trees whose maximal degree is at most Δ^{*} + 1, where Δ^{*} is the degree of some optimal tree for the respective problems. Unless P = NP, this is the best bound achievable in polynomial time.

Original language | English (US) |
---|---|

Pages (from-to) | 409-423 |

Number of pages | 15 |

Journal | Journal of Algorithms |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1994 |

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### All Science Journal Classification (ASJC) codes

- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics

### Cite this

*Journal of Algorithms*,

*17*(3), 409-423. https://doi.org/10.1006/jagm.1994.1042

}

*Journal of Algorithms*, vol. 17, no. 3, pp. 409-423. https://doi.org/10.1006/jagm.1994.1042

**Approximating the minimum-degree steiner tree to within one of optimal.** / Furer, Martin; Raghavachari, Balaji.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximating the minimum-degree steiner tree to within one of optimal

AU - Furer, Martin

AU - Raghavachari, Balaji

PY - 1994/1/1

Y1 - 1994/1/1

N2 - The problem of constructing a spanning tree for a graph G = (V, E) with n vertices whose maximal degree is the smallest among all spanning trees of G is considered. This problem is easily shown to be NP-hard. In the Steiner version of this problem, along with the input graph, a set of distinguished vertices D ⊆ V is given. A minimum-degree Steiner tree is a tree of minimum degree which spans at least the set D. Iterative polynomial time approximation algorithms for the problems are given. The algorithms compute trees whose maximal degree is at most Δ* + 1, where Δ* is the degree of some optimal tree for the respective problems. Unless P = NP, this is the best bound achievable in polynomial time.

AB - The problem of constructing a spanning tree for a graph G = (V, E) with n vertices whose maximal degree is the smallest among all spanning trees of G is considered. This problem is easily shown to be NP-hard. In the Steiner version of this problem, along with the input graph, a set of distinguished vertices D ⊆ V is given. A minimum-degree Steiner tree is a tree of minimum degree which spans at least the set D. Iterative polynomial time approximation algorithms for the problems are given. The algorithms compute trees whose maximal degree is at most Δ* + 1, where Δ* is the degree of some optimal tree for the respective problems. Unless P = NP, this is the best bound achievable in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=0000245114&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000245114&partnerID=8YFLogxK

U2 - 10.1006/jagm.1994.1042

DO - 10.1006/jagm.1994.1042

M3 - Article

AN - SCOPUS:0000245114

VL - 17

SP - 409

EP - 423

JO - Journal of Algorithms

JF - Journal of Algorithms

SN - 0196-6774

IS - 3

ER -