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.

References in zbMATH (referenced in 19 articles , 1 standard article )

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  1. San Segundo, Pablo; Lopez, Alvaro; Artieda, Jorge; Pardalos, Panos M.: A parallel maximum clique algorithm for large and massive sparse graphs (2017)
  2. San Segundo, Pablo; Lopez, Alvaro; Pardalos, Panos M.: A new exact maximum clique algorithm for large and massive sparse graphs (2016)
  3. Wang, Yang; Hao, Jin-Kao; Glover, Fred; Lü, Zhipeng; Wu, Qinghua: Solving the maximum vertex weight clique problem via binary quadratic programming (2016)
  4. Lewko, Mark: An improved lower bound related to the Furstenberg-Sárközy theorem (2015)
  5. Rossi, Ryan A.; Gleich, David F.; Gebremedhin, Assefaw H.: Parallel maximum clique algorithms with applications to network analysis (2015)
  6. San Segundo, Pablo; Nikolaev, Alexey; Batsyn, Mikhail: Infra-chromatic bound for exact maximum clique search (2015)
  7. Wu, Qinghua; Hao, Jin-Kao: A review on algorithms for maximum clique problems (2015)
  8. Acuña, V.; Ferreira, C.E.; Freire, A.S.; Moreno, E.: Solving the maximum edge biclique packing problem on unbalanced bipartite graphs (2014)
  9. Maslov, Evgeny; Batsyn, Mikhail; Pardalos, Panos: Speeding up branch and bound algorithms for solving the maximum clique problem (2014)
  10. Rysz, Maciej; Mirghorbani, Mohammad; Krokhmal, Pavlo; Pasiliao, Eduardo L.: On risk-averse maximum weighted subgraph problems (2014)
  11. San Segundo, Pablo; Tapia, Cristobal: Relaxed approximate coloring in exact maximum clique search (2014)
  12. Szabó, Sándor; Zavalnij, Bogdán: Coloring the edges of a directed graph (2014)
  13. Szabó, Sándor; Zaválnij, Bogdán: Coloring the nodes of a directed graph (2014)
  14. Segundo, Pablo San; Matia, Fernando; Rodriguez-Losada, Diego; Hernando, Miguel: An improved bit parallel exact maximum clique algorithm (2013)
  15. Li, Chu Min; Zhu, Zhu; Manyà, Felip; Simon, Laurent: Optimizing with minimum satisfiability (2012)
  16. Smith, Derek H.; Montemanni, Roberto: A new table of permutation codes (2012)
  17. Segundo, Pablo San; Rodríguez-Losada, Diego; Jiménez, Agustín: An exact bit-parallel algorithm for the maximum clique problem (2011)
  18. Wang, I-Lin; Chang, Chia-Yuan: Mathematical properties and bounds on haplotyping populations by pure parsimony (2011)
  19. Konc, Janez; Janežić, Dušanka: An improved branch and bound algorithm for the maximum clique problem (2007)