2 research outputs found
Robust clustering oracle and local reconstructor of cluster structure of graphs
Due to the massive size of modern network data, local algorithms that run in
sublinear time for analyzing the cluster structure of the graph are receiving
growing interest. Two typical examples are local graph clustering algorithms
that find a cluster from a seed node with running time proportional to the size
of the output set, and clusterability testing algorithms that decide if a graph
can be partitioned into a few clusters in the framework of property testing.
In this work, we develop sublinear time algorithms for analyzing the cluster
structure of graphs with noisy partial information. By using conductance based
definitions for measuring the quality of clusters and the cluster structure, we
formalize a definition of noisy clusterable graphs with bounded maximum degree.
The algorithm is given query access to the adjacency list to such a graph. We
then formalize the notion of robust clustering oracle for a noisy clusterable
graph, and give an algorithm that builds such an oracle in sublinear time,
which can be further used to support typical queries (e.g., IsOutlier(),
SameCluster()) regarding the cluster structure of the graph in sublinear
time. All the answers are consistent with a partition of in which all but a
small fraction of vertices belong to some good cluster. We also give a local
reconstructor for a noisy clusterable graph that provides query access to a
reconstructed graph that is guaranteed to be clusterable in sublinear time. All
the query answers are consistent with a clusterable graph which is guaranteed
to be close to the original graph