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 edge set of the
initial graph). Compared to the main randomized algorithm of
Harchol-Balter, Leighton, and Lewin, the time complexity is
reduced from O(\log^2n) 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_0|\log ^2 n ).