### Citations

1253 |
Approximation algorithms
- Vazirani
- 2004
(Show Context)
Citation Context ... admits a PTAS, but in general graphs it does not. It does however admit an approximation factor. A simple approximation algorithm is to compute a minimum spanning tree, which is a factor 2 algorithm =-=[9]-=-. The best known approximation factor has been gradually decreased from 2 to the 1.55 presented below. The following table shows some of the development: Year Ratio Authors 1993 1.834 Zelikovsky [10] ... |

748 | Some optimal inapproximability results
- Håstad
- 2001
(Show Context)
Citation Context ...m which solves a particular NP-hard problem. Consider the maximum satisfiability problem of linear equations modulo 2 with three variables per equation, MAXE3-LIN-2. The theorem below, due to H˚astad =-=[4]-=-, describes the NP-hard problem that we consider and is defined by an instance of MAX-E3-LIN-2. Theorem 5. For every ɛ > 0 there is an integer k such that it is NP-hard to tell whether a set of n line... |

117 |
An 11/6-approximation algorithm for the network Steiner problem." Algorithmica 9.5
- Zelikovsky
- 1993
(Show Context)
Citation Context ...m [9]. The best known approximation factor has been gradually decreased from 2 to the 1.55 presented below. The following table shows some of the development: Year Ratio Authors 1993 1.834 Zelikovsky =-=[10]-=- 1994 1.746 Berman, Ramaiyer [1] 1996 1.693 Zelikovsky [11] 1997 1.667 Prömel, Steger [6] 1997 1.644 Karpinski, Zelikovsky [5] 1998 1.598 Hougardy, Prömel [3] 2000 1.550 Robins, Zelikovsky [7] The fin... |

107 |
Improved approximations for the Steiner tree problem
- Berman, Ramaiyer
- 1992
(Show Context)
Citation Context ...on factor has been gradually decreased from 2 to the 1.55 presented below. The following table shows some of the development: Year Ratio Authors 1993 1.834 Zelikovsky [10] 1994 1.746 Berman, Ramaiyer =-=[1]-=- 1996 1.693 Zelikovsky [11] 1997 1.667 Prömel, Steger [6] 1997 1.644 Karpinski, Zelikovsky [5] 1998 1.598 Hougardy, Prömel [3] 2000 1.550 Robins, Zelikovsky [7] The final paper by Robins and Zelikovsk... |

49 | Better approximation bounds for the network and Euclidean Steiner tree problems
- Zelikovsky
- 1995
(Show Context)
Citation Context ...ly decreased from 2 to the 1.55 presented below. The following table shows some of the development: Year Ratio Authors 1993 1.834 Zelikovsky [10] 1994 1.746 Berman, Ramaiyer [1] 1996 1.693 Zelikovsky =-=[11]-=- 1997 1.667 Prömel, Steger [6] 1997 1.644 Karpinski, Zelikovsky [5] 1998 1.598 Hougardy, Prömel [3] 2000 1.550 Robins, Zelikovsky [7] The final paper by Robins and Zelikovsky and their algorithm is th... |

48 | New approximation algorithms for the Steiner tree problems
- Karpinski, Zelikovsky
- 1997
(Show Context)
Citation Context ... shows some of the development: Year Ratio Authors 1993 1.834 Zelikovsky [10] 1994 1.746 Berman, Ramaiyer [1] 1996 1.693 Zelikovsky [11] 1997 1.667 Prömel, Steger [6] 1997 1.644 Karpinski, Zelikovsky =-=[5]-=- 1998 1.598 Hougardy, Prömel [3] 2000 1.550 Robins, Zelikovsky [7] The final paper by Robins and Zelikovsky and their algorithm is the main topic of this paper. The non-existence of a PTAS (given the ... |

41 |
The k-Steiner Ratio in Graphs
- Borchers, Du
- 1995
(Show Context)
Citation Context ...CA is based on optimal k-restricted Steiner trees. Thus, the results we are able to obtain, critically depend on the ratio optk opt . Let ρk be the worst-case ratio of optk opt . It has been shown in =-=[2]-=- that ρk ≤ 1 + 1 . (1) ⌊log2 k⌋ + 1 Theorem 2. Algorithm k-LCA has an approximation ratio of at most (1 + 1 4 2 ln( − 1))ρk. ρk Proof. Since our distance function is metric, mst ≤ 2opt, see [9]. Thus,... |

17 |
Improved steiner tree approximation
- Robins, Zelikovsky
(Show Context)
Citation Context ...kovsky [10] 1994 1.746 Berman, Ramaiyer [1] 1996 1.693 Zelikovsky [11] 1997 1.667 Prömel, Steger [6] 1997 1.644 Karpinski, Zelikovsky [5] 1998 1.598 Hougardy, Prömel [3] 2000 1.550 Robins, Zelikovsky =-=[7]-=- The final paper by Robins and Zelikovsky and their algorithm is the main topic of this paper. The non-existence of a PTAS (given the assumption co-RP�=NP) and a lower bound on the best possible appro... |

7 |
Approximation Algorithms for the Steiner Tree
- GRÖPL, HOUGARDY, et al.
(Show Context)
Citation Context ...Year Ratio Authors 1993 1.834 Zelikovsky [10] 1994 1.746 Berman, Ramaiyer [1] 1996 1.693 Zelikovsky [11] 1997 1.667 Prömel, Steger [6] 1997 1.644 Karpinski, Zelikovsky [5] 1998 1.598 Hougardy, Prömel =-=[3]-=- 2000 1.550 Robins, Zelikovsky [7] The final paper by Robins and Zelikovsky and their algorithm is the main topic of this paper. The non-existence of a PTAS (given the assumption co-RP�=NP) and a lowe... |

2 |
RNC-Approximation Algorithms for the Steiner
- Prömmel, Steger
- 1997
(Show Context)
Citation Context ... presented below. The following table shows some of the development: Year Ratio Authors 1993 1.834 Zelikovsky [10] 1994 1.746 Berman, Ramaiyer [1] 1996 1.693 Zelikovsky [11] 1997 1.667 Prömel, Steger =-=[6]-=- 1997 1.644 Karpinski, Zelikovsky [5] 1998 1.598 Hougardy, Prömel [3] 2000 1.550 Robins, Zelikovsky [7] The final paper by Robins and Zelikovsky and their algorithm is the main topic of this paper. Th... |

1 | On the Approximability of the Steiner Tree Problem”, Theor - Thimm - 2003 |