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Handbook of Combinatorial Optimization pp 1249–1291Cite as

Faster and Space Efficient Exact Exponential Algorithms: Combinatorial and Algebraic Approaches

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Abstract

Exponential algorithms, whose time complexity is O(c n) for some constant c > 1, are inevitable when exactly solving NP-complete problems unless \(\mathbf{P} = \mathbf{NP}\). This chapter presents recently emerged combinatorial and algebraic techniques for designing exact exponential time algorithms. The discussed techniques can be used either to derive faster exact exponential algorithms or to significantly reduce the space requirements while without increasing the running time. For illustration, exact algorithms arising from the use of these techniques for some optimization and counting problems are given.

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Acknowledgements

This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00302, the National Natural Science Foundation of China Grant 61103186, 61073174, 61033001, 61061130540, the Hi-Tech research and Development Program of China Grant 2006AA10Z216, and Hong Kong RGC-GRF grants 714009E and 714311.

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Authors and Affiliations

  1. Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, People’s Republic of China

    Dongxiao Yu

  2. Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People’s Republic of China

    Yuexuan Wang

  3. Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People’s Republic of China

    Qiang-Sheng Hua

  4. Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, People’s Republic of China

    Francis C.M. Lau

Authors
  1. Dongxiao Yu
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  2. Yuexuan Wang
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  3. Qiang-Sheng Hua
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  4. Francis C.M. Lau
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Corresponding authors

Correspondence to Dongxiao Yu , Yuexuan Wang , Qiang-Sheng Hua or Francis C.M. Lau .

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Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

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Yu, D., Wang, Y., Hua, QS., Lau, F.C. (2013). Faster and Space Efficient Exact Exponential Algorithms: Combinatorial and Algebraic Approaches. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_38

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