A decentralized algorithm for spectral analysis
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Waiting for a Bat to Fly By (in Polynomial Time)
Combinatorics, Probability and Computing
A decentralized algorithm for spectral analysis
Journal of Computer and System Sciences
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We observe a certain random process on a graph "locally", i.e., in the neighborhood of a node, and would like to derive information about "global" properties of the graph. For example, what can we know about a graph based on observing the returns of a random walk to a given node?Our main result concerns a graph embedded in an orientable surface with genus g, and a process, consisting of random excitations of edges and random balancing around nodes and faces. It is shown how to obtain the genus of the surface in polynomial time from local observations of the process restricted to a connected subgraph whose size is (essentially)O(g2).