1 research outputs found
A Near-optimal Algorithm for Edge Connectivity-based Hierarchical Graph Decomposition
Driven by many applications in graph analytics, the problem of computing
-edge connected components (-ECCs) of a graph for a user-given
has been extensively studied recently. In this paper, we investigate the
problem of constructing the hierarchy of edge connectivity-based graph
decomposition, which compactly represents the -ECCs of a graph for all
possible values. This is based on the fact that each -ECC is entirely
contained in a -ECC. In contrast to the existing approaches that conduct
the computation either in a bottom-up or a top-down manner, we propose a binary
search-based framework which invokes a -ECC computation algorithm as a black
box. Let be the time complexity of computing all -ECCs of
for a specific value. We prove that the time complexity of our framework is
, where is
the degeneracy of and equals the maximum value among the minimum vertex
degrees of all subgraphs of . As is typically small for
real-world graphs, this time complexity is optimal up to a logarithmic factor