We give a randomized fixed parameter tractable algorithm to approximately count the number of copies of a k-vertex graph with bounded treewidth in an n vertex graph. As a consequence, we get randomized algorithms with running time kO(k)nO(1), approximation ratio 1/kO(k), and error probability 2-nO(1) for (a) approximately counting the number of matchings of size k in an n vertex graph and (b) approximately counting the number of paths of length k in an n vertex graph. Our algorithm is based on the Karp-Luby approximate counting technique [8] applied to fixed parameter tractable problems, and the color-coding technique of Alon, Yuster and Zwick [1]. We also show some W-hardness results for parameterized exact counting problems. © Springer-Verlag Berlin Heidelberg 2002.
CITATION STYLE
Arvind, V., & Raman, V. (2002). Approximation algorithms for some parameterized counting problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2518 LNCS, pp. 453–464). https://doi.org/10.1007/3-540-36136-7_40
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