Deterministic Decentralized Search in Random Graphs.

We study a general framework for decentralized search in random graphs. Our main focus is on deterministic memoryless search algorithms that use only local information to reach their destination in a bounded number of steps in expectation. This class includes (with small modifications) the search algorithms used in Kleinberg's pioneering work on long-range percolation graphs and hierarchical network models. We give a characterization of searchable graphs in this model, and use this characterization to prove a monotonicity property for searchability.