Abstract | We consider the problem of searching for a piece of
information in a fully interconnected computer network
(also called a complete network or clique) by exploiting
advice about its location from the network nodes. Each
node contains a database that ?knows? what kind of
documents or information are stored in other nodes
(e.g., a node could be a Web server that answers queries
about documents stored on the Web). The databases in
each node, when queried, provide a pointer that leads to
the node that contains the information. However, this
information is up-to-date (or correct) with some
bounded probability. While, in principle, one may always
locate the information by simply visiting the network
nodes in some prescribed ordering, this requires a time
complexity in the order of the number of nodes of the
network. In this paper, we provide algorithms for locating
an information node in the complete communication
network, which take advantage of advice given from
network nodes. The nodes may either give correct advice,
by pointing directly to the information node, or give
wrong advice, by pointing elsewhere. On the lowerbounds?
side, we show that no fixed-memory (i.e., with
memory independent of the network size) deterministic
algorithm may locate the information node in a constant
(independent of the network size) expected number of
steps. Moreover, if p (1/n) is the probability that a
node of an n-node clique gives correct advice, we show
that no algorithm may locate the information node in an
expected number of steps less than 1/p o(1). To study
how the expected number of steps is affected by the
amount of memory allowed to the algorithms, we give a
memoryless randomized algorithm with expected number
of steps 4/p o(1/p) o(1) and a 1-bit randomized
algorithm requiring on the average at most 2/p o(1)
steps. In addition, in the memoryless case, we also
prove a 4/p lower bound for the expected number of
steps in the case where the nodes giving faulty advice
may decide on the content of this advice in any possible
way and not merely at random (adversarial fault model).
Finally, for the case where faulty nodes behave randomly,
we give an optimal, unlimited memory deterministic
algorithm with expected number of steps bounded
from above by 1/p o(1/p) 1. |