Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
The impact of edge deletions on the number of errors in networks
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Memory lower bounds for randomized collaborative search and implications for biology
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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In this paper, we present a randomized algorithm for a mobile agent to search for an item stored at a node t of a network, without prior knowledge of its exact location. Each node of the network has a database that will answer queries of the form ''how do I find t?'' by responding with the first edge on a shortest path to t. It may happen that some nodes, called liars, give bad advice. We investigate a simple memoryless algorithm which follows the advice with some fixed probability q1/2 and otherwise chooses a random edge. If the degree of each node and number of liars k are bounded, we show that the expected number of edges traversed by the agent before finding t is bounded from above by O(d+r^k), where d is the distance between the initial and target nodes and r=q1-q. We also show that this expected number of steps can be significantly improved for particular topologies such as the complete graph and the torus.