A novel sample space refinement strategy to obtain a smaller sample space, and a star-based sampling approach that addresses both of the main objectives of obtaining a small sample space and reducing the cost of sample trials are proposed.
We develop a new algorithm for counting the number of subgraphs of a network isomorphic to a given query graph (#SubgraphIsomorphism), motivated by network motif search. High-degree vertices (hubs), common in real-world networks, contribute to a combinatorial explosion in the number of subgraphs, making existing motif...
This work presents a novel algorithm named HP-MC that, like prior approaches, is based on the branch and bound search, but which outperforms the leading maximum clique codes on large sparse graphs of various topologies by up to 10x on average.
Given an undirected, unweighted graph $G = (V,E)$ with $n$ vertices and $m$ edges, the triangle counting problem seeks the number of three-cycles in it. Triangle and subgraph counting are classical problems in graph algorithms, central to applications such as community detection, computing the clustering coefficient, m...
Asaf Etgar, A. Gilbert, Quan-Quan C. Liu et al.· 0 citations
Density decomposition characterizes the multi-level dense structure of large networks and supports a wide range of graph mining applications. Given a graph
G = (V, E)
, it assigns each vertex an integral dense number (IDN) and produces a nested sequence of layers D
0
⊇ D
1
⊇ ... ⊇ D
p
that capture increasingl...
Ya-Long Zhang, Rong-Hua Li, Qi Zhang et al.· Proceedings of the ACM on Ma...· 0 citations
A divide-and-conquer-based algorithm is proposed, which not only reduces the search space but also has an improved time complexity and is up to two orders of magnitude faster than the state-of-the-art.
Triangle counting is one of the most fundamental problems in network analysis. Given the massive sizes of real-world graphs, there is a long history of small-space streaming algorithms providing accurate estimates for this problem. However, most of the results focus on estimating the total triangle count or the number...
Cristian Boldrin, C. Seshadhri· 0 citations
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