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## Improved Steiner Tree Approximation in Graphs (2000)

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Citations: | 219 - 6 self |

### Citations

715 |
Matching Theory
- Lovász, Plummer
- 1986
(Show Context)
Citation Context ...phs with edge weights 1 and 2. Bern and Plassmann [4] proved that this problem is MAX SNP-hard and gave a 4 3 -approximation algorithm. Applying Lovasz's algorithm for the parity matroid problem (see =-=[15]-=-), an 1.2875approximation algorithm was given in [3]. We will show that the performance ratio of algorithm k-LCA approaches 1.28 for such graphs, improving on previously achievable bounds. The Iterate... |

425 |
The Steiner Tree Problem
- Hwang, Richards, et al.
- 1992
(Show Context)
Citation Context ...cost subtree spanning the distinguished vertices. Steiner trees are important in various applications such as VLSI routing [13], wirelength estimation [6], phylogenetic tree reconstruction in biology =-=[10]-=-, and network routing [11]. The Steiner Tree Problem is NP -hard even in the Euclidean or rectilinear metrics [8]. Arora established that Euclidean and rectilinear minimum-cost Steiner trees can be ef... |

390 | Polynomial Time Approximation Schemes for Euclidean Traveling Salesman and Other Geometric Problems
- Arora
- 1998
(Show Context)
Citation Context ... is NP -hard even in the Euclidean or rectilinear metrics [8]. Arora established that Euclidean and rectilinear minimum-cost Steiner trees can be efficiently approximated arbitrarily close to optimal =-=[1]-=-. On the other hand, unless P = NP , the Steiner Tree Problem in general graphs cannot be approximated within a factor of 1 + ffl for sufficiently small ffl ? 0 [4, 7]. For arbitrary weighted graphs, ... |

277 |
An approximate solution for the Steiner problem in graphs
- Takashami, Matsuyama
- 1983
(Show Context)
Citation Context ...or sufficiently small ffl ? 0 [4, 7]. For arbitrary weighted graphs, the best Steiner approximation ratio achievable within polynomial time was gradually decreased from 2 to 1:59 in a series of works =-=[19, 20, 2, 21, 17, 14, 9]-=-. In this paper we present a polynomial-time approximation scheme with a performance ratio approaching 1 + ln 3 2s1:55 which improves upon the previously best-known ratio of 1.59 due to Hougardy and P... |

117 |
An 11/6-approximation algorithm for the network Steiner problem." Algorithmica 9.5
- Zelikovsky
- 1993
(Show Context)
Citation Context ...or sufficiently small ffl ? 0 [4, 7]. For arbitrary weighted graphs, the best Steiner approximation ratio achievable within polynomial time was gradually decreased from 2 to 1:59 in a series of works =-=[19, 20, 2, 21, 17, 14, 9]-=-. In this paper we present a polynomial-time approximation scheme with a performance ratio approaching 1 + ln 3 2s1:55 which improves upon the previously best-known ratio of 1.59 due to Hougardy and P... |

107 |
Improved approximations for the Steiner tree problem
- Berman, Ramaiyer
- 1992
(Show Context)
Citation Context ...or sufficiently small ffl ? 0 [4, 7]. For arbitrary weighted graphs, the best Steiner approximation ratio achievable within polynomial time was gradually decreased from 2 to 1:59 in a series of works =-=[19, 20, 2, 21, 17, 14, 9]-=-. In this paper we present a polynomial-time approximation scheme with a performance ratio approaching 1 + ln 3 2s1:55 which improves upon the previously best-known ratio of 1.59 due to Hougardy and P... |

94 | A New Class of Iterative Steiner Tree Heuristics With Good Performance
- Kahng, Robins
- 1992
(Show Context)
Citation Context ...aza, Atlanta, GA, 30303, alexz@cs.gsu.edu. This work was supported in part by a Packard Foundation Fellowship, and by a GSU Research Initiation Grant. 1 that a well-known Iterated 1-Steiner heuristic =-=[12, 13]-=- achieves an approximation ratio of 1:5 for quasi-bipartite graphs; previously, no non-trivial bounds were known for the Iterated 1-Steiner heuristic. Finally, we improve the approximation ratio achie... |

84 |
On optimal interconnections for VLSI
- Kahng, Robins
- 1995
(Show Context)
Citation Context ...iously best-known ratio of 4 3 [4]. Our method is considerably simpler and easier to implement than previous approaches. Our techniques can also be used to prove that the Iterated 1-Steiner heuristic =-=[13]-=- achieves an approximation ratio of 1:5 in quasi-bipartite graphs, thus providing the first known nontrivial performance ratio of this well-known method. 1 Introduction Given an arbitrary weighted gra... |

49 | Better approximation bounds for the network and Euclidean Steiner tree problems
- Zelikovsky
- 1995
(Show Context)
Citation Context |

48 | New approximation algorithms for the Steiner tree problems - Karpinski, Zelikovsky - 1997 |

41 |
The k-Steiner Ratio in Graphs
- Borchers, Du
- 1995
(Show Context)
Citation Context ...timate of the performance ratio of algorithm k-LCA in arbitrary graphs is based on the estimates of optimal k-restricted Steiner trees. Let ae k be the worst-case ratio of opt k opt . It was shown in =-=[5]-=- that ae ks1 + (blog 2 kc + 1) \Gamma1 . We will show below that the approximation ratio of k-LCA is at most ae k (1 + 1 2 ln( 4 ae k \Gamma 1)). Therefore, the approximation ratio of k-LCA converges ... |

38 |
The Rectilinear Steiner problem is NP-complete
- Garey, Johnson
- 1977
(Show Context)
Citation Context ... routing [13], wirelength estimation [6], phylogenetic tree reconstruction in biology [10], and network routing [11]. The Steiner Tree Problem is NP -hard even in the Euclidean or rectilinear metrics =-=[8]-=-. Arora established that Euclidean and rectilinear minimum-cost Steiner trees can be efficiently approximated arbitrarily close to optimal [1]. On the other hand, unless P = NP , the Steiner Tree Prob... |

37 | A 1.598 approximation algorithm for the Steiner problem in graphs - Hougardy, Prömel - 1999 |

36 | New approximation algorithms for the Steiner tree problem - Karpinsky, Zelikovsky - 1995 |

35 | On Wirelength Estimations for Row-Based Placement
- Caldwell, Kahng, et al.
- 1999
(Show Context)
Citation Context ...set, the Steiner Tree Problem asks for a minimum-cost subtree spanning the distinguished vertices. Steiner trees are important in various applications such as VLSI routing [13], wirelength estimation =-=[6]-=-, phylogenetic tree reconstruction in biology [10], and network routing [11]. The Steiner Tree Problem is NP -hard even in the Euclidean or rectilinear metrics [8]. Arora established that Euclidean an... |

25 |
Steiner Trees in VLSI-Layouts
- Korte, Promel, et al.
- 1990
(Show Context)
Citation Context ...distinguished vertices. Steiner trees are important in various applications such as VLSI routing [13], wirelength estimation [6], phylogenetic tree reconstruction in biology [10], and network routing =-=[11]-=-. The Steiner Tree Problem is NP -hard even in the Euclidean or rectilinear metrics [8]. Arora established that Euclidean and rectilinear minimum-cost Steiner trees can be efficiently approximated arb... |

20 |
The Steiner tree problem with edge lengths 1 and 2
- Bern, Plassmann
- 1989
(Show Context)
Citation Context ...approaching 1:5 [18]. For complete graphs with edge weights 1 and 2, we show that our heuristic has an approximation ratio approachings1:28, which improves upon the previously best-known ratio of 4 3 =-=[4]-=-. Our method is considerably simpler and easier to implement than previous approaches. Our techniques can also be used to prove that the Iterated 1-Steiner heuristic [13] achieves an approximation rat... |

20 | A new heuristic for rectilinear Steiner trees
- Mandoiu, Vazirani, et al.
- 1999
(Show Context)
Citation Context ...ve result helps explain why the Iterated 1-Steiner and Rajagopalan-Vazirani heuristics perform similarly when applied to instances of the Steiner Tree Problem restricted to the rectilinear plane (see =-=[16]-=-). Runtime of the algorithm k-LCA in quasi-bipartite graphs. For a given Steiner point v, algorithm k-LCA adds only a full component with the largest gain since the loss is determined by v. We can fin... |

16 | Improved nonapproximability results for minimum vertex cover with density constraints
- Clementi, Trevisan
- 1999
(Show Context)
Citation Context ...imated arbitrarily close to optimal [1]. On the other hand, unless P = NP , the Steiner Tree Problem in general graphs cannot be approximated within a factor of 1 + ffl for sufficiently small ffl ? 0 =-=[4, 7]-=-. For arbitrary weighted graphs, the best Steiner approximation ratio achievable within polynomial time was gradually decreased from 2 to 1:59 in a series of works [19, 20, 2, 21, 17, 14, 9]. In this ... |

7 | Applications of matroid parity problem to approximating steiner trees
- Berman, Furer, et al.
- 1998
(Show Context)
Citation Context ... proved that this problem is MAX SNP-hard and gave a 4 3 -approximation algorithm. Applying Lovasz's algorithm for the parity matroid problem (see [15]), an 1.2875approximation algorithm was given in =-=[3]-=-. We will show that the performance ratio of algorithm k-LCA approaches 1.28 for such graphs, improving on previously achievable bounds. The Iterated 1-Steiner heuristic. The Iterated 1-Steiner heuris... |

7 | Closing the Gap: Near-Optimal Steiner Trees - Griffith, Robins, et al. - 1994 |

6 |
A.: Rnc-approximation algorithms for the steiner problem
- Pramel, Steger
- 1997
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Citation Context |

2 |
On the Bidirected Cut Relaxation for Metric Steiner Problem
- Rajagopalan, Vazirani
- 1999
(Show Context)
Citation Context ....e., in graphs where all nonterminals are pairwise disjoint), our algorithm achieves an approximation ratio ofs1:28, whereas the previously best method achieves an approximation ratio approaching 1:5 =-=[18]-=-. For complete graphs with edge weights 1 and 2, we show that our heuristic has an approximation ratio approachings1:28, which improves upon the previously best-known ratio of 4 3 [4]. Our method is c... |

1 |
Pr ommel, "A 1.598 Approximation Algorithm for the Steiner Problem in Graphs
- Hougardy, J
- 1999
(Show Context)
Citation Context ...et of vertices (terminals). We present a new polynomial-time heuristic with an approximation ratio approaching 1+ ln 3 2s1:55, which improves upon the previously best-known approximation algorithm of =-=[9]-=- with performance ratios1:59. In quasi-bipartite graphs (i.e., in graphs where all nonterminals are pairwise disjoint), our algorithm achieves an approximation ratio ofs1:28, whereas the previously be... |