Abstract
We have already met different types of exponential algorithms. Some of them use only polynomial space, among them in particular the branching algorithms. On the other hand, there are exponential time algorithms needing exponential space, among them in particular the dynamic programming algorithms. In real life applications polynomial space is definitely preferable to exponential space. However, often a “moderate” usage of exponential space can be tolerated if it can be used to speed up the running time. Is it possible by sacrificing a bit of running time to gain in space? In the first section of this chapter we discuss such an interpolation between the two extremes of space complexity for dynamic programming algorithms. In the second section we discuss an opposite technique to gain time by using more space, in particular for branching algorithms.
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References
Robson, J.M.: Algorithms for maximum independent sets. Journal of Algorithms 7(3), 425–440 (1986)
Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. J. Comput. System. Sci. 4, 177–192 (1970)
Gurevich, Y., Shelah, S.: Expected computation time for Hamiltonian path problem. SIAM J. Comput. 16(3), 486–502 (1987)
Bodlaender, H.L., Fomin, F.V., Koster, A.M.C.A., Kratsch, D., Thilikos, D.M.: On exact algorithms for treewidth. In: Proceedings of the 14th Annual European Symposium on Algorithms (ESA 2006), Lecture Notes in Comput. Sci., vol. 4168, pp. 672–683. Springer (2006)
Björklund, A., Husfeldt, T.: Exact algorithms for exact satisfiability and number of perfect matchings. Algorithmica 52(2), 226–249 (2008)
Bodlaender, H.L., Kratsch, D.: An exact algorithm for graph coloring with polynomial memory. Technical Report UU-CS-2006-015, University of Utrecht (March 2006)
Koivisto, M., Parviainen, P.: A space—time tradeoff for permutation problems. In: Proceedings of the 21th ACM-SIAM Symposium on Discrete Algorithms (SODA 2010), pp. 484–493. ACM and SIAM (2010)
Bourgeois, N., Croce, F.D., Escoffier, B., Paschos, V.T.: Exact algorithms for dominating clique problems. In: Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009), Lecture Notes in Comput. Sci., vol. 5878, pp. 4–13. Springer (2009)
Fomin, F.V., Grandoni, F., Kratsch, D.: Some new techniques in design and analysis of exact (exponential) algorithms. Bulletin of the EATCS 87, 47–77 (2005)
Sunil Chandran, L., Grandoni, F.: Refined memorization for vertex cover. Inf. Process. Lett. 93(3), 125–131 (2005)
Fomin, F.V., Grandoni, F., Kratsch, D.: A measure & conquer approach for the analysis of exact algorithms. J. ACM 56(5) (2009)
Kratsch, D., Liedloff, M.: An exact algorithm for the minimum dominating clique problem. Theor. Comput. Sci. 385(1-3), 226–240 (2007)
Fomin, F.V., Gaspers, S., Saurabh, S., Stepanov, A.A.: On two techniques of combining branching and treewidth. Algorithmica 54(2), 181–207 (2009)
Woeginger, G.J.: Open problems around exact algorithms. Discrete Appl. Math. 156(3), 397–405 (2008).
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Fomin, F.V., Kratsch, D. (2010). Time Versus Space. In: Exact Exponential Algorithms. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16533-7_10
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DOI: https://doi.org/10.1007/978-3-642-16533-7_10
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