MaxCliqueDyn

Maximum Clique Algorithm: MaxCliqueDyn is a fast exact algorithm for finding a maximum clique in an undirected graph described in Ref. [1] developed by Janez Konc. A clique is a fully connected subgraph of a graph and a maximum clique is the clique with the largest number of vertices in a given graph. Maximum clique algorithms differ from maximal clique algorithms (e.g., Bron-Kerbosch algorithm). The maximal search is for all maximal cliques in a graph (cliques that cannot be enlarged), while the maximum clique algorithms find a maximum clique (a clique with the largest number of vertices). This makes maximum clique algorithms about an order of magnitude faster.

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References in zbMATH (referenced in 37 articles , 1 standard article )

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  1. Mohammadi, Neda; Kadivar, Mehdi: A local core number based algorithm for the maximum clique problem (2021)
  2. Szabó, Sándor: A clique search problem and its application to machine scheduling (2021)
  3. Walteros, Jose L.; Buchanan, Austin: Why is maximum clique often easy in practice? (2020)
  4. Wang, Yiyuan; Cai, Shaowei; Chen, Jiejiang; Yin, Minghao: SCCWalk: an efficient local search algorithm and its improvements for maximum weight clique problem (2020)
  5. Torres-Jimenez, Jose; Perez-Torres, Jose Carlos: A greedy algorithm to construct covering arrays using a graph representation (2019)
  6. Azarija, Jernej; Marc, Tilen: There is no (75,32,10,16) strongly regular graph (2018)
  7. Li, Chu-Min; Fang, Zhiwen; Jiang, Hua; Xu, Ke: Incremental upper bound for the maximum clique problem (2018)
  8. Li, Chu-Min; Liu, Yanli; Jiang, Hua; Manyà, Felip; Li, Yu: A new upper bound for the maximum weight clique problem (2018)
  9. Rysz, Maciej; Pajouh, Foad Mahdavi; Krokhmal, Pavlo; Pasiliao, Eduardo L.: Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights (2018)
  10. Szabó, Sándor: Estimating clique size by coloring the nodes of auxiliary graphs (2018)
  11. Züge, Alexandre Prusch; Carmo, Renato: On comparing algorithms for the maximum clique problem (2018)
  12. Li, Chu-Min; Jiang, Hua; Manyà, Felip: On minimization of the number of branches in branch-and-bound algorithms for the maximum clique problem (2017)
  13. San Segundo, Pablo; Lopez, Alvaro; Artieda, Jorge; Pardalos, Panos M.: A parallel maximum clique algorithm for large and massive sparse graphs (2017)
  14. Tomita, Etsuji: Efficient algorithms for finding maximum and maximal cliques and their applications (2017)
  15. Torres-Jimenez, Jose; Perez-Torres, Jose Carlos; Maldonado-Martinez, Gildardo: hClique: an exact algorithm for maximum clique problem in uniform hypergraphs (2017)
  16. San Segundo, Pablo; Lopez, Alvaro; Pardalos, Panos M.: A new exact maximum clique algorithm for large and massive sparse graphs (2016)
  17. Tomita, Etsuji; Yoshida, Kohei; Hatta, Takuro; Nagao, Atsuki; Ito, Hiro; Wakatsuki, Mitsuo: A much faster branch-and-bound algorithm for finding a maximum clique (2016)
  18. Wang, Yang; Hao, Jin-Kao; Glover, Fred; Lü, Zhipeng; Wu, Qinghua: Solving the maximum vertex weight clique problem via binary quadratic programming (2016)
  19. Lewko, Mark: An improved lower bound related to the Furstenberg-Sárközy theorem (2015)
  20. Pattabiraman, Bharath; Patwary, Md. Mostofa Ali; Gebremedhin, Assefaw H.; Liao, Wei-Keng; Choudhary, Alok: Fast algorithms for the maximum clique problem on massive graphs with applications to overlapping community detection (2015)

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