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FOCS

2006

IEEE

2006

IEEE

We consider the minimum cost spanning tree problem under the restriction that all degrees must be at most a given value k. We show that we can efﬁciently ﬁnd a spanning tree of maximum degree at most k + 2 whose cost is at most the cost of the optimum spanning tree of maximum degree at most k. This is almost best possible. The approach uses a sequence of simple algebraic, polyhedral and combinatorial arguments. It illustrates many techniques and ideas in combinatorial optimization as it involves polyhedral characterizations, uncrossing, matroid intersection, and graph orientations (or packing of spanning trees). The result generalizes to the setting where every vertex has both upper and lower bounds and gives then a spanning tree which violates the bounds by at most two units and whose cost is at most the cost of the optimum tree. It also gives a better understanding of the subtour relaxation for both the symmetric and asymmetric traveling salesman problems. The generalization to ...

Related Content

Added |
11 Jun 2010 |

Updated |
11 Jun 2010 |

Type |
Conference |

Year |
2006 |

Where |
FOCS |

Authors |
Michel X. Goemans |

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