ALCOMFT-TR-01-105

Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc and Yannis C. Stamatiou
Locating Information with Uncertainty in Fully Interconnected Networks: The Case of Non-Distributed Memory
Patras. Work package 2. May 2001.

Abstract: \beginabstract

\noindent We consider the problem of searching for a piece of information in a fully interconnected computer 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, that 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 lower bounds side, we show that no finite memory deterministic algorithm may locate the information node in finite expected number of steps. In addition, if the probability that a node gives correct advice is p and p tends to 0 while it is asymptotically larger than 1/n, we show that no algorithm may locate the information node in expected number of steps less than 1/p. In order 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 and a 1-bit randomized algorithm requiring on the average at most 2/p steps. Finally, we give an optimal, unlimited memory deterministic algorithm with expected number of steps equal to 1/p.

Postscript file: ALCOMFT-TR-01-105.ps.gz (97 kb).