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

  • Dongxiao YuEmail author
  • Yuexuan WangEmail author
  • Qiang-Sheng HuaEmail author
  • Francis C.M. LauEmail author
Reference work entry


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.


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.



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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of Hong KongHong KongPeople’s Republic of China
  2. 2.Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijingPeople’s Republic of China
  3. 3.Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijingPeople’s Republic of China
  4. 4.Department of Computer ScienceThe University of Hong KongHong KongPeople’s Republic of China

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