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 33 articles , 1 standard article )

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  1. Wang, Yiyuan; Cai, Shaowei; Chen, Jiejiang; Yin, Minghao: SCCWalk: an efficient local search algorithm and its improvements for maximum weight clique problem (2020)
  2. Torres-Jimenez, Jose; Perez-Torres, Jose Carlos: A greedy algorithm to construct covering arrays using a graph representation (2019)
  3. Azarija, Jernej; Marc, Tilen: There is no (75,32,10,16) strongly regular graph (2018)
  4. Li, Chu-Min; Fang, Zhiwen; Jiang, Hua; Xu, Ke: Incremental upper bound for the maximum clique problem (2018)
  5. Li, Chu-Min; Liu, Yanli; Jiang, Hua; Manyà, Felip; Li, Yu: A new upper bound for the maximum weight clique problem (2018)
  6. Rysz, Maciej; Pajouh, Foad Mahdavi; Krokhmal, Pavlo; Pasiliao, Eduardo L.: Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights (2018)
  7. Szabó, Sándor: Estimating clique size by coloring the nodes of auxiliary graphs (2018)
  8. Züge, Alexandre Prusch; Carmo, Renato: On comparing algorithms for the maximum clique problem (2018)
  9. 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)
  10. San Segundo, Pablo; Lopez, Alvaro; Artieda, Jorge; Pardalos, Panos M.: A parallel maximum clique algorithm for large and massive sparse graphs (2017)
  11. Tomita, Etsuji: Efficient algorithms for finding maximum and maximal cliques and their applications (2017)
  12. Torres-Jimenez, Jose; Perez-Torres, Jose Carlos; Maldonado-Martinez, Gildardo: hClique: an exact algorithm for maximum clique problem in uniform hypergraphs (2017)
  13. San Segundo, Pablo; Lopez, Alvaro; Pardalos, Panos M.: A new exact maximum clique algorithm for large and massive sparse graphs (2016)
  14. 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)
  15. Wang, Yang; Hao, Jin-Kao; Glover, Fred; Lü, Zhipeng; Wu, Qinghua: Solving the maximum vertex weight clique problem via binary quadratic programming (2016)
  16. Lewko, Mark: An improved lower bound related to the Furstenberg-Sárközy theorem (2015)
  17. Rossi, Ryan A.; Gleich, David F.; Gebremedhin, Assefaw H.: Parallel maximum clique algorithms with applications to network analysis (2015)
  18. San Segundo, Pablo; Nikolaev, Alexey; Batsyn, Mikhail: Infra-chromatic bound for exact maximum clique search (2015)
  19. Wu, Qinghua; Hao, Jin-Kao: A review on algorithms for maximum clique problems (2015)
  20. Acuña, V.; Ferreira, C. E.; Freire, A. S.; Moreno, E.: Solving the maximum edge biclique packing problem on unbalanced bipartite graphs (2014)

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