## Approximating the minimum-degree Steiner tree to within one of optimal (1994)

Venue: | Journal of Algorithms |

Citations: | 72 - 5 self |

### BibTeX

@ARTICLE{Raghavachari94approximatingthe,

author = {Balaji Raghavachari},

title = {Approximating the minimum-degree Steiner tree to within one of optimal},

journal = {Journal of Algorithms},

year = {1994},

volume = {17},

pages = {409--423}

}

### Years of Citing Articles

### OpenURL

### Abstract

some optimal tree for the respective problems. Unless P = N P, this is the best bound achievable in polynomial time.

### Citations

8521 |
Introduction to Algorithms
- Cormen, Stein, et al.
- 2001
(Show Context)
Citation Context ...one from the optimal degree. Each phase of the algorithm can be implemented in nearly linear time using Tarjan's fast disjoint set union-find algorithm for maintaining connected components (e.g., see =-=[9]-=-). Therefore the entire algorithm runs in O(mnff(m; n) log n), where m is the number of edges and ff is the inverse Ackerman function. 5 The Steiner Problem The Steiner version of the MDST problem is ... |

275 |
Every planar map is four-colorable
- Appel, Haken
- 1976
(Show Context)
Citation Context ...in an additive term of one. The only other NP-hard problems which we know to have similar approximation properties are the edge coloring problem [16], [23] and the 3-coloring problem in planar graphs =-=[1]-=-, [15]. In this paper, we show that Win's result [24] implies that the inverse of the toughness is approximately equal to \Delta \Lambda . We provide an approximation algorithm which runs in polynomia... |

211 | When trees collide: An approximation algorithmfor the generalized Steiner problem on networks
- AGRAWAL, KLEIN, et al.
- 1991
(Show Context)
Citation Context ... reliable networks of small maximal degree. Additionally, this problem is interesting in its own right. Recently there has been a flurry of activity on approximating various NP-complete problems [2], =-=[3]-=-, [4], [11], [18], [19], [22]. Our result shows that the minimum-degree spanning tree problem is approximable within an additive term of one. The only other NP-hard problems which we know to have simi... |

68 |
Approximating the minimum-degree spanning tree to within one from the optimal degree
- Fürer, Raghavachari
- 1992
(Show Context)
Citation Context ... be approximated in polynomial time to within a factor of O(log n) of the degree of an 7soptimal tree. They also provide approximations for computing the toughness of a graph. F"urer and Raghavachari =-=[12]-=- provided an approximation algorithm for the Steiner problem which produces a tree of degree O(\Delta \Lambdas+ log n) in polynomial time. In this section, we provide an approximation algorithm which ... |

46 |
Approximation through multicommodity flow. Foundations of Computer Science
- Klein, Agrawal, et al.
- 1990
(Show Context)
Citation Context ... need reliable networks of small maximal degree. Additionally, this problem is interesting in its own right. Recently there has been a flurry of activity on approximating various NP-complete problems =-=[2]-=-, [3], [4], [11], [18], [19], [22]. Our result shows that the minimum-degree spanning tree problem is approximable within an additive term of one. The only other NP-hard problems which we know to have... |

19 |
Ordering problems approximated: single-processor scheduling and interval graph completion
- Ravi, Agrawal, et al.
- 1991
(Show Context)
Citation Context ...able networks of small maximal degree. Additionally, this problem is interesting in its own right. Recently there has been a flurry of activity on approximating various NP-complete problems [2], [3], =-=[4]-=-, [11], [18], [19], [22]. Our result shows that the minimum-degree spanning tree problem is approximable within an additive term of one. The only other NP-hard problems which we know to have similar a... |

17 |
Complexity of spanning tree problems
- Camerini, Galbiati, et al.
- 1980
(Show Context)
Citation Context ...less P = N P , this is the best bound achievable in polynomial time. 1 Introduction Various problems of computing spanning trees of graphs that satisfy given constraints have been studied before [6], =-=[7]-=-, [8], [20]. Depending on the constraints, they have been characterized by different complexity classes. Though the problem of computing a minimum cost spanning tree in a graph with edge weights is ef... |

11 |
An implementation of reliable broadcast using an unreliable multicast facility
- Garcia-Molina, Kogan
- 1988
(Show Context)
Citation Context ...ful in the computation of spanning trees in networks for non-critical broadcast. Solutions to the broadcast problem have mainly concentrated on how to complete the broadcasting as quickly as possible =-=[13]-=-. But there are instances like the distribution of mail and news on the Internet, in which the broadcast need not be executed on a priority basis. One of the parameters that different sites may want t... |

6 |
How tough is the minimum-degree Steiner tree? A new approximate min-max equality
- Agrawal, Klein, et al.
- 1991
(Show Context)
Citation Context ..., University of Texas at Dallas, Box 830688, Richardson, TX 750830688. E-mail: rbk@utdallas.edu 1sthe minimum-degree Steiner tree problem when D = V . In another earlier work, Agrawal, Klein and Ravi =-=[5]-=- have shown that even the more general minimum-degree Steiner tree problem can be approximated to within a log n factor in polynomial time. Recently Ravi, Raghavachari and Klein [21] have given approx... |

5 |
On the complexity of finding multi-constrained spanning trees
- CAMERINI, GALBIATI, et al.
- 1983
(Show Context)
Citation Context ...P = N P , this is the best bound achievable in polynomial time. 1 Introduction Various problems of computing spanning trees of graphs that satisfy given constraints have been studied before [6], [7], =-=[8]-=-, [20]. Depending on the constraints, they have been characterized by different complexity classes. Though the problem of computing a minimum cost spanning tree in a graph with edge weights is efficie... |

4 |
The bounded path tree problem
- Camerini, Galbiati
- 1982
(Show Context)
Citation Context ...s. Unless P = N P , this is the best bound achievable in polynomial time. 1 Introduction Various problems of computing spanning trees of graphs that satisfy given constraints have been studied before =-=[6]-=-, [7], [8], [20]. Depending on the constraints, they have been characterized by different complexity classes. Though the problem of computing a minimum cost spanning tree in a graph with edge weights ... |

1 |
An NC Approximation Algorithm for the Minimum Degree Spanning Tree Problem
- Math
- 1973
(Show Context)
Citation Context ...en approximation algorithms for minimizing the degree while satisfying more general connectivity requirements (e.g., generalized Steiner trees, T-joins, bridge-connected spanning subgraphs). Chv'atal =-=[10]-=- defined the following notion of toughness of a graph G. Let X ae V be an arbitrary subset of vertices. Suppose the graph induced by V \GammasX contains c(X) connected components. The toughness of a g... |