In this paper we examine the problem of searching for some information item in the nodes of a fully interconnected computer network, where each node contains information relevant to some topic as well as links to other network nodes that also contain information, not necessarily related to locally kept information. These links are used to facilitate the Internet users and mobile software agents that try to locate specific pieces of information. However, the links do not necessarily point to nodes containing information of interest to the user or relevant to the aims of the mobile agent. Thus an element of uncertainty is introduced. For example, when an Internet user or some search agent lands on a particular network node, they see a set of links that point to information that is, supposedly, relevant to the current search. Therefore, we can assume that a link points to relevant information with some unknown probability p that, in general, is related to the number of nodes in the network (intuitively, as the network grows, this probability tends to zero since adding more nodes to the network renders some extant links less accurate or obsolete). Consequently, since there is uncertainty as to whether the links contained in a node?s Web page are correct or not, a search algorithm cannot rely on following the links systematically since it may end up spending too much time visiting nodes that contain irrelevant information. In this work, we will describe and analyze a search algorithm that is only allowed to transfer a fixed amount of memory along communication links as it visits the network nodes. The algorithm is, however, allowed to use one bit of memory at each node as an ?already visited? flag. In this way the algorithm has its memory distributed to the network nodes, avoiding overloading the network links as it moves from node to node searching for the information. We work on fully interconnected networks for simplicity reasons and, moreover, because according to some recent experimental evidence, such networks can be considered to be a good approximation of the current structure of the World Wide Web.