# A Local Clustering Algorithm for Massive Graphs and Its Application to Nearly Linear Time Graph Partitioning

@article{Spielman2013ALC, title={A Local Clustering Algorithm for Massive Graphs and Its Application to Nearly Linear Time Graph Partitioning}, author={Daniel A. Spielman and Shang-Hua Teng}, journal={SIAM J. Comput.}, year={2013}, volume={42}, pages={1-26} }

We study the design of local algorithms for massive graphs. A local graph algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a good cluster---a subset of vertices whose internal connections are significantly richer than its external connections---near a given vertex. The running time of our algorithm, when it finds a nonempty local cluster, is nearly linear in the size of the…

## 314 Citations

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- Computer Science, MathematicsJ. ACM
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A simple randomized local partitioning algorithm that finds a sparse cut by simulating the volume-biased evolving set process, which is a Markov chain on sets of vertices, and proves a bicriteria approximation algorithm for the expansion profile of any graph.

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This work studies a class of algorithms for approximating the sparsest cut in a graph locally, and discovers that procedures based on evolving sets tend to outperform those based on PageRank vectors.

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This work shows how to use LocalImprove to obtain a constant approximation O(OPT) as long as CONN/OPT = Omega(1), the first flow-based algorithm and shows that spectral methods are not the only viable approach to the construction of local graph partitioning algorithm and open door to the study of algorithms with even better approximation and locality guarantees.

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This paper presents a simple and distributed algorithm for graph clustering: for a wide class of graphs that are characterised by a strong cluster-structure, this algorithm finishes in a poly-logarithmic number of rounds, and recovers a partition of the graph close to optimal.

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- Computer ScienceACM Trans. Parallel Comput.
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A simple and distributed algorithm for graph clustering that finishes in a poly-logarithmic number of rounds and recovers a partition of the graph close to optimal for a wide class of graphs characterised by a strong cluster-structure.

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- Computer Science, MathematicsSODA
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This work formalizes the notion of robust clustering oracle for a noisy clusterable graph, and gives an algorithm that builds such an oracle in sublinear time, which can be further used to support typical queries regarding the cluster structure of the graph in sub linear time.

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This work studies local algorithms for finding a pair of vertex sets defined with respect to their inter-connection and their relationship with the rest of the graph using a new reduction technique that relates the structure of multiple sets to a single vertex set in the reduced graph.

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A simple and distributed algorithm for graph clustering for a wide class of graphs that are characterised by a strong cluster-structure, which finishes in a poly-logarithmic number of rounds, and recovers a partition of the graph close to an optimal partition.

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A simple and distributed algorithm for graph clustering for a wide class of graphs that are characterised by a strong cluster-structure, which finishes in a poly-logarithmic number of rounds, and recovers a partition of the graph close to an optimal partition.

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A simple and distributed algorithm for graph clustering for a wide class of graphs that are characterised by a strong cluster-structure, which finishes in a poly-logarithmic number of rounds, and recovers a partition of the graph close to an optimal partition.

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