Enumerating maximum cliques in massive graphs

2020 ◽  
pp. 1-1
Author(s):  
Can Lu ◽  
Jeffrey Xu Yu ◽  
Hao Wei ◽  
Yikai Zhang
Keyword(s):  
Maximum Cliques ◽  
Massive Graphs

scholarly journals SSumM: Sparse Summarization of Massive Graphs

2020 ◽  
Author(s):  
Kyuhan Lee ◽  
Hyeonsoo Jo ◽  
Jihoon Ko ◽  
Sungsu Lim ◽  
Kijung Shin
Keyword(s):  
Massive Graphs

Tiered Sampling

2021 ◽  
Vol 15 (5) ◽  
pp. 1-52
Author(s):  
Lorenzo De Stefani ◽  
Erisa Terolli ◽  
Eli Upfal
Keyword(s):  
Large Scale ◽  
Analysis Of Algorithms ◽  
Base Layer ◽  
Single Edge ◽  
Real World Data ◽  
High Quality ◽  
Large Graphs ◽  
Massive Graphs ◽  
Variance Estimate ◽  
Low Probability

We introduce Tiered Sampling , a novel technique for estimating the count of sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size M , which can be magnitudes smaller than the number of edges. Our methods address the challenging task of counting sparse motifs—sub-graph patterns—that have a low probability of appearing in a sample of M edges in the graph, which is the maximum amount of data available to the algorithms in each step. To obtain an unbiased and low variance estimate of the count, we partition the available memory into tiers (layers) of reservoir samples. While the base layer is a standard reservoir sample of edges, other layers are reservoir samples of sub-structures of the desired motif. By storing more frequent sub-structures of the motif, we increase the probability of detecting an occurrence of the sparse motif we are counting, thus decreasing the variance and error of the estimate. While we focus on the designing and analysis of algorithms for counting 4-cliques, we present a method which allows generalizing Tiered Sampling to obtain high-quality estimates for the number of occurrence of any sub-graph of interest, while reducing the analysis effort due to specific properties of the pattern of interest. We present a complete analytical analysis and extensive experimental evaluation of our proposed method using both synthetic and real-world data. Our results demonstrate the advantage of our method in obtaining high-quality approximations for the number of 4 and 5-cliques for large graphs using a very limited amount of memory, significantly outperforming the single edge sample approach for counting sparse motifs in large scale graphs.

scholarly journals Finding Maximum Cliques on a Quantum Annealer

2017 ◽  
Author(s):  
Guillaume Chapuis ◽  
Hristo Djidjev ◽  
Georg Hahn ◽  
Guillaume Rizk
Keyword(s):  
Maximum Cliques

scholarly journals FAST: FPGA-based Subgraph Matching on Massive Graphs

2021 ◽  
Author(s):  
Xin Jin ◽  
Zhengyi Yang ◽  
Xuemin Lin ◽  
Shiyu Yang ◽  
Lu Qin ◽  
...  
Keyword(s):  
Subgraph Matching ◽  
Massive Graphs

scholarly journals Finding A Small Vertex Cover in Massive Sparse Graphs: Construct, Local Search, and Preprocess

2017 ◽  
Vol 59 ◽  
pp. 463-494 ◽  
Author(s):  
Shaowei Cai ◽  
Jinkun Lin ◽  
Chuan Luo
Keyword(s):  
Local Search ◽  
Real World ◽  
Large Scale ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Vertex Cover ◽  
Search Algorithms ◽  
Theory And Practice ◽  
Sparse Graphs ◽  
Massive Graphs

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard combinatorial optimization problem of great importance in theory and practice. Due to its NP-hardness, there has been much interest in developing heuristic algorithms for finding a small vertex cover in reasonable time. Previously, heuristic algorithms for MinVC have focused on solving graphs of relatively small size, and they are not suitable for solving massive graphs as they usually have high-complexity heuristics. This paper explores techniques for solving MinVC in very large scale real-world graphs, including a construction algorithm, a local search algorithm and a preprocessing algorithm. Both the construction and search algorithms are based on low-complexity heuristics, and we combine them to develop a heuristic algorithm for MinVC called FastVC. Experimental results on a broad range of real-world massive graphs show that, our algorithms are very fast and have better performance than previous heuristic algorithms for MinVC. We also develop a preprocessing algorithm to simplify graphs for MinVC algorithms. By applying the preprocessing algorithm to local search algorithms, we obtain two efficient MinVC solvers called NuMVC2+p and FastVC2+p, which show further improvement on the massive graphs.

scholarly journals Two-goal Local Search and Inference Rules for Minimum Dominating Set

2020 ◽  
Author(s):  
Shaowei Cai ◽  
Wenying Hou ◽  
Yiyuan Wang ◽  
Chuan Luo ◽  
Qingwei Lin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Inference Rules ◽  
Local Search Algorithm ◽  
Minimum Dominating Set ◽  
Massive Graphs ◽  
Construction Procedure ◽  
Almost All ◽  
Main Ideas

Minimum dominating set (MinDS) is a canonical NP-hard combinatorial optimization problem with applications. For large and hard instances one must resort to heuristic approaches to obtain good solutions within reasonable time. This paper develops an efficient local search algorithm for MinDS, which has two main ideas. The first one is a novel local search framework, while the second is a construction procedure with inference rules. Our algorithm named FastDS is evaluated on 4 standard benchmarks and 3 massive graphs benchmarks. FastDS obtains the best performance for almost all benchmarks, and obtains better solutions than state-of-the-art algorithms on massive graphs.

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