Robust Critical Node Selection by Benders Decomposition

Published Online:https://doi.org/10.1287/ijoc.2015.0671

References

  • Addis B, Summa MD, Grosso A (2013) Identifying critical nodes in undirected graphs: Complexity results and polynomial algorithms for the case of bounded treewidth. Discrete Appl. Math. 161(16–17):2349–2360.CrossrefGoogle Scholar
  • Arulselvan A, Commander CW, Pardalos PM, Shylo O (2007) Managing network risk via critical node identification. Gülpınar N, Rustem B, eds. Risk Management in Telecommunication Networks (Springer, Berlin), 474–477.Google Scholar
  • Arulselvan A, Commander CW, Shylo O, Pardalos PM (2011) Cardinality-constrained critical node detection problem. Gülpınar N, Harrison P, Rustem B, eds. Performance Models and Risk Management CommunicationSystems, Springer Optimization and Its Applications, Vol. 46 (Springer, New York), 79–91.CrossrefGoogle Scholar
  • Ben-Tal A, Ghaoui LE, Nemirovski A (2009) Robust Optimization, Princeton Series in Applied Mathematics (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1):238–252.CrossrefGoogle Scholar
  • Bertsimas D, Sim M (2004a) The price of robustness. Oper. Res. 52(1):35–53.LinkGoogle Scholar
  • Bertsimas D, Sim M (2004b) Robust discrete optimization under ellipsoidal uncertainty sets. Technical report, Massachusetts Institute of Technology, Cambridge, MA. http://web.mit.edu/dbertsim/www/papers.html.Google Scholar
  • Cohen R, Havlin S, Ben-Avraham D (2003) Efficient immunization strategies for computer networks and populations. Phys. Rev. Lett. 91(24):247901–247905.CrossrefGoogle Scholar
  • Commander CW, Pardalos PM, Ryabchenko V, Uryasev S, Zrazhevsky G (2007) The wireless network jamming problem. J. Combinatorial Optim. 14(4):481–498.CrossrefGoogle Scholar
  • Di Summa M, Grosso A, Locatelli M (2011) Complexity of the critical node problem over trees. Comput. Oper. Res. 38(12):1766–1774.CrossrefGoogle Scholar
  • Di Summa M, Grosso A, Locatelli M (2012) Branch and cut algorithms for detecting critical nodes in undirected graphs. Comput. Optim. Appl. 53(3):649–680.CrossrefGoogle Scholar
  • Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math. Programming 91(2):201–213.CrossrefGoogle Scholar
  • Fan N, Pardalos PM (2010a) Linear and quadratic programming approaches for the general graph partitioning problem. J. Global Optim. 48(1):57–71.CrossrefGoogle Scholar
  • Fan N, Pardalos PM (2010b) Robust optimization of graph partitioning and critical node detection in analyzing networks. Wu W, Daescu O, eds. Combinatorial Optim. Appl., Lecture Notes in Computer Science, Vol. 6508 (Springer, Berlin), 170–183.CrossrefGoogle Scholar
  • Fan N, Zheng QP, Pardalos PM (2012) Robust optimization of graph partitioning involving interval uncertainty. Theoret. Comput. Sci. 447:53–61.CrossrefGoogle Scholar
  • Floyd R (1962) Algorithm 97: Shortest path. Comm. ACM 5(6):345.CrossrefGoogle Scholar
  • Garg N, Vazirani VV, Yannakakis M (1996) Approximate max-flow min-(multi) cut theorems and their applications. SIAM J. Comput. 25(2):235–251.CrossrefGoogle Scholar
  • Geoffrion AM (1972) Generalized Benders decomposition. J. Optim. Theory Appl. 10(4):237–260.CrossrefGoogle Scholar
  • Ghaddar B, Anjos M, Liers F (2011) A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem. Ann. Oper. Res. 188(1):155–174.CrossrefGoogle Scholar
  • Hopcroft J, Tarjan R (1973) Efficient algorithms for graph manipulation. Comm. ACM 16(6):372–378.CrossrefGoogle Scholar
  • Li M, Gabriel SA, Shim Y, Azarm S (2011) Interval uncertainty-based robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning. Networks Spatial Econom. 11(1):159–191.CrossrefGoogle Scholar
  • Magnanti TL, Wong RT (1981) Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Oper. Res. 29(3):464–484.LinkGoogle Scholar
  • Montemanni R (2006) A Benders decomposition approach for the robust spanning tree problem with interval data. Eur. J. Oper. Res. 174(3):1479–1490.CrossrefGoogle Scholar
  • Naoum-Sawaya J, Elhedhli S (2013) An interior-point Benders based branch-and-cut algorithm for mixed integer programs. Ann. Oper. Res. 210(1):33–55.CrossrefGoogle Scholar
  • Saito H, Murota K (2007) Benders decomposition approach to robust mixed integer programming. Pacific J. Optim. 3(1):99–112.Google Scholar
  • Shen S, Smith JC (2012) Polynomial-time algorithms for solving a class of critical node problems on trees and series-parallel graphs. Networks 60(2):103–119.CrossrefGoogle Scholar
  • Shen S, Smith JC, Goli R (2012) Exact interdiction models and algorithms for disconnecting networks via node deletions. Discrete Optim. 9(3):172–188.CrossrefGoogle Scholar
  • Siddiqui S, Azarm S, Gabriel S (2011) A modified Benders decomposition method for efficient robust optimization under interval uncertainty. Structural Multidisciplinary Optim. 44(2):259–275.CrossrefGoogle Scholar
  • Siddiqui S, Gabriel SA, Azarm S (2014) Solving mixed-integer robust optimization problems with interval uncertainty using Benders decomposition. J. Oper. Res. Soc. 66(4):664–673.CrossrefGoogle Scholar
  • Tao Z, Zhongqian F, Binghong W (2006) Epidemic dynamics on complex networks. Progress Natural Sci. 16(5):452–457.CrossrefGoogle Scholar
  • Ventresca M (2012) Global search algorithms using a combinatorial unranking-based problem representation for the critical node detection problem. Comput. Oper. Res. 39(11):2763–2775.CrossrefGoogle Scholar
  • Ventresca M, Aleman D (2014) A derandomized approximation algorithm for the critical node detection problem. Comput. Oper. Res. 43:261–270.CrossrefGoogle Scholar
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