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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.

Keywords

  • Travel Salesman Problem
  • Travel Salesman Problem
  • Exact Algorithm
  • Hamiltonian Cycle
  • Steiner Tree Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

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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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