## Abstract

The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with non-negative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. We consider the on-line generalized Steiner problem, in which pairs of vertices arrive on-line and are needed to be connected immediately. We give a simple O(log n) competitive deterministic on-line algorithm. The previous best online algorithm (by Westbrook and Yan) was O(√n log n) competitive. We also consider the network connectivity leasing problem which is a generalization of the GSP. Here edges of the graph can be either bought or leased for different costs. We provide simple randomized O(log^{2} n) competitive algorithm based on the on-line generalized Steiner problem result.

Original language | American English |
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Title of host publication | Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 |

Publisher | Association for Computing Machinery |

Pages | 68-74 |

Number of pages | 7 |

ISBN (Electronic) | 0898713668 |

State | Published - 28 Jan 1996 |

Externally published | Yes |

Event | 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 - Atlanta, United States Duration: 28 Jan 1996 → 30 Jan 1996 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | Part F129447 |

### Conference

Conference | 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 |
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Country/Territory | United States |

City | Atlanta |

Period | 28/01/96 → 30/01/96 |

### Bibliographical note

Funding Information:‘Johns Hopkins University and Lab. for Computer ence, MIT. Supported by NSF contract 9114440-CCR, ARPA/Army contract DABT63-93-C-0038, ARPA/Air Force Contract F19628-95-C-0137, and NIST/USRA Contract 5555. 47. E-Mail: baruch@cs.jhu.edu. ‘Department of Computer Science, Tel University ,Tel-Aviv 69978, Israel. Research supported part by Allon Fellowship and by the Israel Science Foundation admimistered by the Israel Academy of Sciences. E-Mail: azarQmath.tau.ac.il. *Department of Computer Science, Tel-Aviv University, Tel-Aviv 69978, Israel. Research supported in part by Ben Gu-rion Fellowship, the Ministry of Science and Arts. E-Mail: yairb@math.tau.ac.il.