Michael Mitzenmacher, joint work with Hossein Esfandiari
Metric Sublinear Algorithms via Linear Sampling
In this work we provide a new technique to design fast approximation
algorithms for graph problems where the points of the graph lie in a
metric space. Specifically, we present a sampling approach for such
metric graphs that, using a sublinear number of edge weight queries,
provides a linear sampling, where each edge is (roughly speaking)
sampled proportionally to its weight. For several natural problems,
such as densest subgraph and max cut among others, we show that by
sparsifying the graph using this sampling process, we can run a
suitable approximation algorithm on the sparsified graph and the
result remains a good approximation for the original problem. Our
results have several interesting implications, such as providing the
first sublinear time approximation algorithm for densest subgraph in a
metric space, and improving the running time of estimating the average
distance.