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Novel Approaches for Analyzing Biological Networks

Author

Listed:
  • Balabhaskar Balasundaram

    (Texas A&M University)

  • Sergiy Butenko

    (Texas A&M University)

  • Svyatoslav Trukhanov

    (Texas A&M University)

Abstract

This paper proposes clique relaxations to identify clusters in biological networks. In particular, the maximum n-clique and maximum n-club problems on an arbitrary graph are introduced and their recognition versions are shown to be NP-complete. In addition, integer programming formulations are proposed and the results of sample numerical experiments performed on biological networks are reported.

Suggested Citation

  • Balabhaskar Balasundaram & Sergiy Butenko & Svyatoslav Trukhanov, 2005. "Novel Approaches for Analyzing Biological Networks," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 23-39, August.
    • Handle: RePEc:spr:jcomop:v:10:y:2005:i:1:d:10.1007_s10878-005-1857-x
    DOI: 10.1007/s10878-005-1857-x
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    References listed on IDEAS

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    1. Stanislav Busygin & Sergiy Butenko & Panos M. Pardalos, 2002. "A Heuristic for the Maximum Independent Set Problem Based on Optimization of a Quadratic Over a Sphere," Journal of Combinatorial Optimization, Springer, vol. 6(3), pages 287-297, September.
    2. R. Luce & Albert Perry, 1949. "A method of matrix analysis of group structure," Psychometrika, Springer;The Psychometric Society, vol. 14(2), pages 95-116, June.
    3. Robert Mokken, 1979. "Cliques, clubs and clans," Quality & Quantity: International Journal of Methodology, Springer, vol. 13(2), pages 161-173, April.
    4. R. Luce, 1950. "Connectivity and generalized cliques in sociometric group structure," Psychometrika, Springer;The Psychometric Society, vol. 15(2), pages 169-190, June.
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    Citations

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    Cited by:

    1. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    2. Chitra Balasubramaniam & Sergiy Butenko, 2017. "On robust clusters of minimum cardinality in networks," Annals of Operations Research, Springer, vol. 249(1), pages 17-37, February.
    3. Oleksandra Yezerska & Foad Mahdavi Pajouh & Alexander Veremyev & Sergiy Butenko, 2019. "Exact algorithms for the minimum s-club partitioning problem," Annals of Operations Research, Springer, vol. 276(1), pages 267-291, May.
    4. Shahram Shahinpour & Sergiy Butenko, 2013. "Algorithms for the maximum k-club problem in graphs," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 520-554, October.
    5. Veremyev, Alexander & Boginski, Vladimir, 2012. "Identifying large robust network clusters via new compact formulations of maximum k-club problems," European Journal of Operational Research, Elsevier, vol. 218(2), pages 316-326.
    6. Alexander Veremyev & Vladimir Boginski & Eduardo Pasiliao, 2015. "Analytical characterizations of some classes of optimal strongly attack-tolerant networks and their Laplacian spectra," Journal of Global Optimization, Springer, vol. 61(1), pages 109-138, January.
    7. Hannes Moser & Rolf Niedermeier & Manuel Sorge, 2012. "Exact combinatorial algorithms and experiments for finding maximum k-plexes," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 347-373, October.
    8. Svyatoslav Trukhanov & Chitra Balasubramaniam & Balabhaskar Balasundaram & Sergiy Butenko, 2013. "Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations," Computational Optimization and Applications, Springer, vol. 56(1), pages 113-130, September.
    9. Foad Mahdavi Pajouh & Balabhaskar Balasundaram & Illya V. Hicks, 2016. "On the 2-Club Polytope of Graphs," Operations Research, INFORMS, vol. 64(6), pages 1466-1481, December.
    10. Almeida, Maria Teresa & Carvalho, Filipa D., 2014. "An analytical comparison of the LP relaxations of integer models for the k-club problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 489-498.
    11. Alexander Veremyev & Oleg A. Prokopyev & Sergiy Butenko & Eduardo L. Pasiliao, 2016. "Exact MIP-based approaches for finding maximum quasi-cliques and dense subgraphs," Computational Optimization and Applications, Springer, vol. 64(1), pages 177-214, May.
    12. Carvalho, Filipa D. & Almeida, M. Teresa, 2011. "Upper bounds and heuristics for the 2-club problem," European Journal of Operational Research, Elsevier, vol. 210(3), pages 489-494, May.
    13. Komusiewicz, Christian & Nichterlein, André & Niedermeier, Rolf & Picker, Marten, 2019. "Exact algorithms for finding well-connected 2-clubs in sparse real-world graphs: Theory and experiments," European Journal of Operational Research, Elsevier, vol. 275(3), pages 846-864.
    14. Buchanan, Austin & Sung, Je Sang & Boginski, Vladimir & Butenko, Sergiy, 2014. "On connected dominating sets of restricted diameter," European Journal of Operational Research, Elsevier, vol. 236(2), pages 410-418.
    15. Grigory Pastukhov & Alexander Veremyev & Vladimir Boginski & Eduardo L. Pasiliao, 2014. "Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 462-486, April.
    16. Maciej Rysz & Foad Mahdavi Pajouh & Pavlo Krokhmal & Eduardo L. Pasiliao, 2018. "Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights," Annals of Operations Research, Springer, vol. 262(1), pages 89-108, March.
    17. Balasundaram, Balabhaskar & Borrero, Juan S. & Pan, Hao, 2022. "Graph signatures: Identification and optimization," European Journal of Operational Research, Elsevier, vol. 296(3), pages 764-775.
    18. Veremyev, Alexander & Boginski, Vladimir & Pasiliao, Eduardo L. & Prokopyev, Oleg A., 2022. "On integer programming models for the maximum 2-club problem and its robust generalizations in sparse graphs," European Journal of Operational Research, Elsevier, vol. 297(1), pages 86-101.
    19. Yajun Lu & Hosseinali Salemi & Balabhaskar Balasundaram & Austin Buchanan, 2022. "On Fault-Tolerant Low-Diameter Clusters in Graphs," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3181-3199, November.
    20. Foad Mahdavi Pajouh & Esmaeel Moradi & Balabhaskar Balasundaram, 2017. "Detecting large risk-averse 2-clubs in graphs with random edge failures," Annals of Operations Research, Springer, vol. 249(1), pages 55-73, February.
    21. Zhuqi Miao & Balabhaskar Balasundaram, 2020. "An Ellipsoidal Bounding Scheme for the Quasi-Clique Number of a Graph," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 763-778, July.
    22. Yezerska, Oleksandra & Mahdavi Pajouh, Foad & Butenko, Sergiy, 2017. "On biconnected and fragile subgraphs of low diameter," European Journal of Operational Research, Elsevier, vol. 263(2), pages 390-400.
    23. Andrew C. Trapp & Oleg A. Prokopyev, 2010. "Solving the Order-Preserving Submatrix Problem via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 387-400, August.
    24. Veremyev, Alexander & Prokopyev, Oleg A. & Boginski, Vladimir & Pasiliao, Eduardo L., 2014. "Finding maximum subgraphs with relatively large vertex connectivity," European Journal of Operational Research, Elsevier, vol. 239(2), pages 349-362.

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