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Exact exponential algorithms

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Abstract

Discovering surprises in the face of intractability.

References

  1. Bax, E.T. Inclusion and exclusion algorithm for the Hamiltonian path problem. Inf. Process, Lett. 47, 4 (1993), 203--207. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Bellman, R. Dynamic Programming, Princeton University Press, 1957.Google ScholarGoogle Scholar
  3. Bellman, R. Dynamic programming treatment of the travelling salesman problem. J. ACM 9 (1962), 61--63. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Björklund, A. Determinant sums for undirected hamiltonicity. In Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS 2010) (2010), IEEE, 173--182. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M. Narrow sieves for parameterized paths and packings. arXiv:1007.1161 (2010).Google ScholarGoogle Scholar
  6. Björklund, A., Husfeldt, T., Koivisto, M. Set partitioning via inclusion-exclusion. SIAM J. Comput. 39, 2 (2009), 546--563. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Coppersmith, D., Winograd, S. Matrix multiplication via arithmetic progressions. J. Symbolic Comput. 9, 3 (1990), 251--280. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Cygan, M., Nederlof, J., Pilipczuk, M., Pilipczuk, M., van Rooij, J.M.M., Wojtaszczyk, J.O. Solving connectivity problems parameterized by treewidth in single exponential time. In Proceedings of the 52nd Annual Symposium on Foundations of ComputerScience (2011), IEEE, 150--159. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Dantsin, E., Hirsch, E.A. Worst-case upper bounds. In Handbook of Satisfiability, volume 185 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2009, 403--424.Google ScholarGoogle Scholar
  10. Downey, R.G., Fellows, M.R. Parameterized Complexity, Springer, 1999.Google ScholarGoogle Scholar
  11. Eppstein, D. Small maximal independent sets and faster exact graph coloring. J. Graph Algorithms Appl. 7, 2 (2003), 131--140.Google ScholarGoogle ScholarCross RefCross Ref
  12. Eppstein, D. Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms. ACM Trans. Algorithms 2, 4 (2006), 492--509. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Flum, J., Grohe, M. Parameterized Complexity Theory, Springer, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Fomin, F.V., Grandoni, F., Kratsch, D. A measure&conquer approach for the analysis of exact algorithms. J. ACM 56, 5 (2009). Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Fomin, F.V., Kratsch, D. Exact Exponential Algorithms, Springer, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Fortnow, L. The status of the P versus NP problem. Commun. ACM 52, 9 (2009), 78--86. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Garey, M.R., Johnson, D.S. Computers and Intractability, A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, 1979. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Golomb, S.W., Baumert, L.D. Backtrack programming. J. ACM 12 (1965), 516--524. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Held, M., Karp, R.M. A dynamic programming approach to sequencing problems. J. Soc. Indust. Appl. Math. 10 (1962), 196--210.Google ScholarGoogle ScholarCross RefCross Ref
  20. Holyer, I. The NP-completeness of edge-coloring. SIAM J. Comput. 10, 4 (1981), 718--720.Google ScholarGoogle Scholar
  21. Husfeldt, T. Invitation to algorithmic uses of inclusion--exclusion. arXiv:1105.2942 (2011). Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Itai, A., Rodeh, M. Finding a minimum circuit in a graph. SIAM J. Comput. 7, 4 (1978), 413--423.Google ScholarGoogle ScholarCross RefCross Ref
  23. Karp, R.M. Dynamic programming meets the principle of inclusion and exclusion. Oper. Res. Lett. 1, 2 (1982), 49--51. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Knuth, D.E. The Art of Computer Programming, vol. 2: Seminumerical Algorithms, 3rd edn, Addison-Wesley, 1998. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Kohn, S., Gottlieb, A., Kohn, M. A generating function approach to the traveling salesman problem. In Proceedings of the ACM Annual Conference (ACM 1977) (1977), ACM Press, 294--300. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Koivisto, M. Optimal 2-constraint satisfaction via sum-product algorithms. Inform. Process. Lett. 98, 1 (2006), 24--28. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Lawler, E.L. A note on the complexity of the chromatic number problem. Inf. Process. Lett. 5, 3 (1976), 66--67.Google ScholarGoogle ScholarCross RefCross Ref
  28. Malik, S., Zhang, L. Boolean satisfiability: From theoretical hardness to practical success. Commun. ACM 52, 8 (2009), 76--82. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Moon, J.W., Moser, L. On cliques in graphs. Israel J. Math. 3 (1965), 23--28.Google ScholarGoogle ScholarCross RefCross Ref
  30. Mulmuley, K., Vazirani, U.V., Vazirani, V.V. Matching is as easy as matrix inversion. Combinatorica 7, 1 (1987), 105--113. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Niedermeier, R. Invitation to Fixed-Parameter Algorithms, Oxford University Press, 2006.Google ScholarGoogle Scholar
  32. Strassen, V. Gaussian elimination is not optimal. Numer. Math. 13 (1969), 354--356.Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Vassilevska Williams, V. Multiplying matrices faster than Coppersmith-Winograd. In Proceedings of 44th ACM Symposium on Theory of Computing (STOC 2012) (2012), ACM, 887--898. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Vazirani, V.V. Approximation Algorithms, Springer, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Walker, R.J. An enumerative technique for a class of combinatorial problems. In Proceedings of Symposia in Applied Mathematics, vol. 10, American Mathematical Society, 1960, 91--94.Google ScholarGoogle Scholar
  36. Williams, R. A new algorithm for optimal 2-constraint satisfaction and its implications. Theoret. Comput. Sci. 348, 2--3 (2005), 357--365. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Williams, R. Improving exhaustive search implies superpolynomial lower bounds. In Proceedings of 42nd ACM Symposium on Theory of Computing (2010), ACM, 231--240. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Woeginger, G. Exact algorithms for NP-hard problems: a survey. In Combinatorial Optimization - Eureka, You Shrink! (2003), volume 2570 of Lecture Notes in Computer Science, Springer, 185--207. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Woeginger, G. Space and time complexity of exact algorithms: some open problems. In Proceedings of the 1st International Workshop on Parameterized and Exact Computation (2004), volume 3162 of Lecture Notes in Computer Science, Springer, 281--290.Google ScholarGoogle ScholarCross RefCross Ref
  40. Yates, F. The Design and Analysis of Factorial Experiments, Imperial Bureau of Soil Science, 1937.Google ScholarGoogle Scholar
  41. Zykov, A.A. On some properties of linear complexes. Mat. Sbornik N.S. 24, 66 (1949), 163--188.Google ScholarGoogle Scholar

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        cover image Communications of the ACM
        Communications of the ACM  Volume 56, Issue 3
        March 2013
        93 pages
        ISSN:0001-0782
        EISSN:1557-7317
        DOI:10.1145/2428556
        Issue’s Table of Contents

        Copyright © 2013 ACM

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        • Published: 1 March 2013

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