Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-23T11:43:09.568Z Has data issue: false hasContentIssue false
  • English
  • Français

Counting Unlabelled Subtrees of a Tree is #P-complete

Published online by Cambridge University Press:  01 February 2010

Leslie Ann Goldberg  and
Mark Jerrum
Leslie Ann Goldberg
Affiliation:
Department of Computer Science, University of Warwick, Coventry, CV4 7AL, [email protected], http://www.dcs.warwick.ac.uk/~leslie/
Mark Jerrum
Affiliation:
Department of Computer Science, University of Edinburgh, The King's Buildings, Edinburgh EH9 3JZ, [email protected], http://www.dcs.ed.ac.uk/~mrj/

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of counting unlabelled subtrees of a tree (that is, sub-trees that are distinct up to isomorphism) is #P-complete, and hence equivalent in computational difficulty to evaluating the permanent of a 0,1-matrix.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 3 , 2000 , pp. 117 - 124
Copyright
Copyright © London Mathematical Society 2000

References

1. Blache, G., Karpinski, M. and Wirtgen, J., ‘On approximation intractability of the bandwidth problem’, Electronic Colloquium on Computational Complexity, Report TR98-014, 1998. http://www.eccc.uni-trier.de/eccc-local/Lists/TR-1998.htmlGoogle Scholar
2. Edwards, K. J. and McDiarmid, C. J. H., ‘The complexity of harmonious colouring for trees’, Discrete Appl. Math. 57 (1995) 133–144.CrossRefGoogle Scholar
3. Garey, M. R. and Johnson, D. S., Computers and intractability: a guide to the theory of NP-completeness (Freeman, San Francisco, CA, 1979).Google Scholar
4. Garey, M. R., Graham, R. L., Johnson, D. S. and Knuth, D. E., ‘Complexity results for bandwidth minimization’, SIAM J. Appl. Math. 34 (1978) 477–95.CrossRefGoogle Scholar
5. Harary, F. and Palmer, E. M., Graphical enumeration (Academic Press, 1973).Google Scholar
6. Hopcroft, J. E. and Tarjan, R. E., ‘Efficient planarity testing’, J. ACM 21 (1974) 549–568.CrossRefGoogle Scholar
7. Köbler, J., Schöning, U. and Toran, J., ‘On counting and approximation’, Acta In form. 26 (1989) 363–379.Google Scholar
8. Papadimitriou, C. H., Computational complexity (Addison-Wesley, 1994).Google Scholar
9. Toda, S., ‘PP is as hard as the polynomial-time hierarchy’, SIAM J. Comput. 20 (1991) 865–877.CrossRefGoogle Scholar
10. Toda, S. and Watanabe, O., ‘Polynomial-time 1-Turing reductions from #PH to #P’, Theoret. Comput. Set 100 (1992) 205‘221.Google Scholar
11. Valiant, L. G., ‘The complexity of enumeration and reliability problems’, SIAM J. Comput. 8 (1979) 410–421.Google Scholar
12. Welsh, D. J. A., Complexity: knots, colourings and counting (Cambridge University Press, 1993).CrossRefGoogle Scholar