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Tutorial on Computational Complexity

Author

Listed:
  • Craig A. Tovey

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

Computational complexity measures how much work is required to solve different problems. It provides a useful classification tool for OR/MS practitioners, especially when tackling discrete deterministic problems. Use it to tell, in advance, whether a problem is easy or hard. Knowing this won't solve your problem, but it will help you to decide what kind of solution method is appropriate. Complexity analysis helps you to understand and deal with hard problems. It can pinpoint the nasty parts of your problem, alert you to a special structure you can take advantage of, and guide you to model more effectively. You will solve your problem better when you know the borders between hard and easy. Locating the difficulty can indicate where to aggregate, decompose, or simplify. To detect and prove computational difficulty, show that a known hard problem from the literature is embedded within your problem. Fix parameters of your problem to arrive at the known hard problem, or use specialization, padding, forcing, or the more difficult gadget proofs. Study contrasting pairs of easy and hard problems to develop your intuitive ability to assess complexity.

Suggested Citation

  • Craig A. Tovey, 2002. "Tutorial on Computational Complexity," Interfaces, INFORMS, vol. 32(3), pages 30-61, June.
    • Handle: RePEc:inm:orinte:v:32:y:2002:i:3:p:30-61
    DOI: 10.1287/inte.32.3.30.39
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    References listed on IDEAS

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    1. Arthur M. Geoffrion, 1987. "An Introduction to Structured Modeling," Management Science, INFORMS, vol. 33(5), pages 547-588, May.
    2. Michael W. Carter & Craig A. Tovey, 1992. "When Is the Classroom Assignment Problem Hard?," Operations Research, INFORMS, vol. 40(1-supplem), pages 28-39, February.
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    4. Steven T. Hackman & Robert C. Leachman, 1989. "A General Framework for Modeling Production," Management Science, INFORMS, vol. 35(4), pages 478-495, April.
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    Cited by:

    1. Mavrommatis, George, 2008. "Learning objects and objectives towards automatic learning construction," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1449-1458, June.
    2. Yongjie Yang & Dinko Dimitrov, 2019. "The complexity of shelflisting," Theory and Decision, Springer, vol. 86(1), pages 123-141, February.
    3. Yang, Yongjie & Dimitrov, Dinko, 2023. "Group control for consent rules with consecutive qualifications," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 1-7.
    4. Alexandra M. Newman & Martin Weiss, 2013. "A Survey of Linear and Mixed-Integer Optimization Tutorials," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 26-38, September.
    5. Constantine N. Goulimis, 2007. "ASP, The Art and Science of Practice: Appeal to NP-Completeness Considered Harmful: Does the Fact That a Problem Is NP-Complete Tell Us Anything?," Interfaces, INFORMS, vol. 37(6), pages 584-586, December.
    6. E A Silver, 2004. "An overview of heuristic solution methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 936-956, September.
    7. Milad Zamanifar & Timo Hartmann, 2020. "Optimization-based decision-making models for disaster recovery and reconstruction planning of transportation networks," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 104(1), pages 1-25, October.

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