#### DMCA

## Mining maximal cliques from large graphs using (2012)

### Citations

3439 | MapReduce: simplified data processing on large clusters
- Dean, Ghemawat
(Show Context)
Citation Context ...ve a reasonable turnaround time. In addition, these graphs may not even fit in the memory of a single machine. This motivates the search for parallel and distributed enumeration algorithms. MapReduce =-=[8]-=- is a parallel framework that has recently gained popularity due to its low cost to setup and maintain, the simple interface provided to the programmer, its built-in fault tolerance, and the availabil... |

353 |
Algorithm 457: finding all cliques of an undirected graph.
- Bron, Kerbosch
- 1973
(Show Context)
Citation Context ...tial in the number of vertices [33] and MCE has been proven to be NP-hard [10]. Although this is true in the worst case, not all graphs exhibit this behavior and polynomial time sequential algorithms =-=[2, 3, 6, 10, 11, 12, 18, 20, 29, 39, 40]-=- can be achieved if the number of maximal cliques in the output is polynomial in the input size. Large graphs are becoming more common, such as web [26] and social network [24] graphs. These graphs of... |

237 | Friendship and mobility: user movement in location-based social networks,” in KDD,
- Cho, Myers, et al.
- 2011
(Show Context)
Citation Context ...rge graph database [23], as well as on Erdös-Rényi random graphs. The test graphs used are given in Table 5.1 along with some basic properties. The soc-sign-epinion[24], soc-epinion[35], loc-gowalla=-=[7]-=-, and soc-slashdot0902 [26] graphs represent typical social networks, where vertices represent users and edges represent friendships. cit-patents [15] is a citation graph for U.S. patents granted betw... |

115 |
Arboricity and subgraph listing algorithms,
- Chiba, Nishizeki
- 1985
(Show Context)
Citation Context ...tial in the number of vertices [33] and MCE has been proven to be NP-hard [10]. Although this is true in the worst case, not all graphs exhibit this behavior and polynomial time sequential algorithms =-=[2, 3, 6, 10, 11, 12, 18, 20, 29, 39, 40]-=- can be achieved if the number of maximal cliques in the output is polynomial in the input size. Large graphs are becoming more common, such as web [26] and social network [24] graphs. These graphs of... |

40 | Generating all maximal independant sets: Np-hardness and polynomial time algorithms.
- Lawler, Lenstra, et al.
- 1980
(Show Context)
Citation Context ...and in [28] they are used for mining association rules. Unfortunately, the number of maximal cliques in a graph can be exponential in the number of vertices [33] and MCE has been proven to be NP-hard =-=[10]-=-. Although this is true in the worst case, not all graphs exhibit this behavior and polynomial time sequential algorithms [2, 3, 6, 10, 11, 12, 18, 20, 29, 39, 40] can be achieved if the number of max... |

26 | Finding maximal cliques in massive networks by h*-graph.
- Cheng, Ke, et al.
- 2010
(Show Context)
Citation Context ...Γ(v) ∩ Γ(u)| ≥ (k − 2). Modani and Dey then describe a breadth first search algorithm for enumerating cliques. No theoretical bounds are given and minimal experimental results are shown. Cheng et al. =-=[5]-=- develop the first external memory algorithm for enumerating all maximal cliques in an undirected graph. To do so, they propose the use of the H*-graph to bound memory usage. The authors give bounds o... |

22 |
Listing all maximal cliques in sparse graphs in near-optimal time,”
- Eppstein, Loffler, et al.
- 2010
(Show Context)
Citation Context ...tial in the number of vertices [33] and MCE has been proven to be NP-hard [10]. Although this is true in the worst case, not all graphs exhibit this behavior and polynomial time sequential algorithms =-=[2, 3, 6, 10, 11, 12, 18, 20, 29, 39, 40]-=- can be achieved if the number of maximal cliques in the output is polynomial in the input size. Large graphs are becoming more common, such as web [26] and social network [24] graphs. These graphs of... |

19 | A note on the problem of reporting maximal cliques. - Cazals, Karande - 2008 |

15 |
A parallel algorithm for enumerating all the maximal k-plexes
- Wu, Pei
- 2007
(Show Context)
Citation Context ...actor slower than Tomita et al. on less sparse graphs. 3.2 Review of Parallel Algorithms for MCE Early works in the area of parallel maximal clique enumeration include Zhang et al. [44] and Du et al. =-=[9]-=-. Zhang et al. developed one of the first parallel maximal clique enumeration algorithms. Based on Kose’s algorithm [22], it enumerates k-cliques by combining two cliques of size k − 1, which share k ... |

13 |
A novel approach to structural alignment using realistic structural and environmental information
- Chen, Crippen
(Show Context)
Citation Context ...used to integrate different types of genome mapping data [16]. Several works use maximal cliques in the study of proteins, examining protein interactions, secondary structure, and sequence clustering =-=[4, 13, 21, 32, 43]-=-. In [17] they are used in comparing the chemical structures of two compounds, and in [28] they are used for mining association rules. Unfortunately, the number of maximal cliques in a graph can be ex... |

13 | Listing all maximal cliques in large sparse real-world graphs. - Eppstein, Loffler, et al. - 2013 |

2 |
Accessed on 10 January 2012. Project homepage
- org
(Show Context)
Citation Context ...popularity due to its low cost to setup and maintain, the simple interface provided to the programmer, its built-in fault tolerance, and the availability of open source implementations such as Hadoop =-=[1]-=-. For these reasons, we focus on algorithms that fit the MapReduce model of computation. This work introduces a novel parallel MCE algorithm called PECO (Parallel Enumeration 2of Cliques using Orderin... |