Expander Decomposition and Pruning: Faster, Stronger, and Simpler
Thatchaphol Saranurak, Di Wang

TL;DR
This paper introduces a nearly linear time algorithm for expander decomposition in graphs, enabling efficient clustering with strong connectivity guarantees, and improves dynamic graph maintenance through an advanced pruning technique.
Contribution
It presents the first nearly linear time algorithm for strong expander decomposition with practical parameters, and develops a new expander pruning method for dynamic graphs.
Findings
Algorithm runs in old m/ time for
Achieves strong cluster expansion guarantees in nearly linear time
Develops a practical expander pruning technique for dynamic graph algorithms
Abstract
We study the problem of graph clustering where the goal is to partition a graph into clusters, i.e. disjoint subsets of vertices, such that each cluster is well connected internally while sparsely connected to the rest of the graph. In particular, we use a natural bicriteria notion motivated by Kannan, Vempala, and Vetta which we refer to as {\em expander decomposition}. Expander decomposition has become one of the building blocks in the design of fast graph algorithms, most notably in the nearly linear time Laplacian solver by Spielman and Teng, and it also has wide applications in practice. We design algorithm for the parametrized version of expander decomposition, where given a graph of edges and a parameter , our algorithm finds a partition of the vertices into clusters such that each cluster induces a subgraph of conductance at least (i.e. a expander),…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Complex Network Analysis Techniques
