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

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... d 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 * A preliminary version of this paper appeared in