## Abstract

The resource discovery problem was introduced by Harchol-Balter, Leighton, and Lewin. They developed a number of algorithms for the problem in the weakly connected directed graph model. This model is a directed logical graph that represents the vertices' knowledge about the topology of the underlying communication network. The current paper proposes a deterministic algorithm for the problem in the same model, with improved time, message, and communication complexities. Each previous algorithm had a complexity that was higher at least in one of the measures. Specifically, previous deterministic solutions required either time linear in the diameter of the initial network, or communication complexity O(n^{3}) (with message complexity O(n^{2})), or message complexity O(|E_{0}| log n) (where E_{0} is the arc set of the initial graph G_{0}). Compared with the main randomized algorithm of Harchol-Balter, Leighton, and Lewin, the time complexity is reduced from O(log^{2} n) to O(log n), the message complexity from O(n log^{2} n) to O (n log n), and the communication complexity from O(n^{2} log^{3} n) to O(|E_{2}| log^{2} n). Our work significantly extends the connectivity algorithm of Shiloach and Vishkin which was originally given for a parallel model of computation. Our result also confirms a conjecture of Harchol-Balter, Leighton, and Lewin, and addresses an open question due to Lipton.

Original language | English |
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Pages (from-to) | 479-495 |

Number of pages | 17 |

Journal | Theory of Computing Systems |

Volume | 36 |

Issue number | 5 |

DOIs | |

State | Published - Sep 2003 |

Externally published | Yes |

### Bibliographical note

Funding Information:∗ A preliminary version of this paper appeared in Proc. SPAA ’01, July 4–6, 2001, Hersonissos, Crete. Shay Kutten was supported in part by a grant from the Israel Ministry of Science and Art and by the Technion Fund for the Promotion of Research. David Peleg was supported in part by grants from the Israel Science Foundation and the Israel Ministry of Science and Art. Uzi Vishkin was supported by NSF Grant 9820955.