J. Nesetril and S. Poljak, "On the Complexity of the Subgraph Problem," Commen. Math. Univ. Carol. 26 (1985), 415-419.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of problems in FPT for which the only f are uncomputable are given in [DF93] while [DF95c] describes natural problems in FPT for which the only known f are not known to be computable. The best known method for solving the parameterized Clique problem is the algorithm of Nesetril and Poljak [NP85] that runs in time O(n 2 ffl 3 )k ) where 2 ffl represents the exponent on the time for multiplying two n Theta n matrices (best known is 2:376 : see [CW90] For Dominating Set we know of nothing better than the trivial O(n 1 k ) time algorithm that tries all vertex subsets of size ....

J. Nesetril and S. Poljak. On the complexity of the subgraph problem. Commen. Math. Univ. Carol. 26 (1985), 415--419.

....in the discussion of efforts to develop exponential algorithms that improve significantly on simple exhaustive search. A classic example is the algorithm of Nesetril and Poljak that uses fast matrix multiplication to solve the k Clique problem for n vertex graphs in time O(n ck c 0:792 [NP85]. A weakness of the parameterized complexity program is that some of the most general and spectacular positive methods, such as the celebrated results of Robertson and Seymour [RS85] yield algorithms having parameter functions that are supremely impractical (e.g. towers of 2 s of height ....

J. Nesetril and S. Poljak, "On the Complexity of the Subgraph Problem," Comm. Math. Univ. Carol. 26 (1985), 415--419.

....to H [4] As we shall see, the existential and constructive problems do not necessarily have the same complexity. Previous work on fixed subgraph isomorphism has concentrated on recognizing specific families of subgraphs, such as small paths [1, 3, 11] cycles [4, 10, 11, 15, 16] and cliques [12]. A practical algorithm for subgraph isomorphism, without analysis, is presented by [19] In Section 2, we consider the complexity of recognizing paths of length k. This leads to a more general algorithm for fixed subgraph isomorphism, presented in Section 3, whose time complexity is sensitive to ....

....multiplication can be used to efficiently compute 16 subgraph dense graphs sparse graphs ) 10] 16] O(m ) O(mn) K 4 O(n ff 1 Table 1: Current bounds for recognizing certain subgraphs. P k for k 5. We note that matrix multiplication is the basis of Nesetril and Poljak s [12] O(n dk Deltaff=3e ) algorithm for recognizing arbitrary subgraphs on k vertices, where ff is the exponent in the fast matrix multiplication algorithm. 5 Conclusions We have presented a new algorithm for fixed subgraph isomorphism in arbitrary graphs, which runs in O(n m) time, where f is ....

J. Nesetril and S. Poljak. On the complexity of the subgraph problem. Commen. Math. Univ. Carol., 26:415--419, 1985.

.... results concerning the computational complexity of the parameterized versions of these problems: 1) for each fixed value of the parameter k, Vertex Cover is solvable in linear time [2] 2) for each fixed value of the parameter k, the best known algorithm for Clique runs in time O(n 2k=3 ) [18]. In this paper, by a parameterized problem we mean a computational problem whose input includes a positive integer parameter that we will invariably denote by k. A parameterized problem is said to be fixed parameter tractable if it is solvable in time f(k)n ff for each fixed parameter value k, ....

J. Nesetr'il and S. Poljak, On the complexity of the subgraph problem, Commen. Math. 11 Univ. Carol., vol. 26 (1985), pp. 415--419.

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J. Nesetril and S. Poljak, "On the Complexity of the Subgraph Problem," Commen. Math. Univ. Carol. 26 (1985), 415-419.

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J. Nesetril and S. Poljak, "On the Complexity of the Subgraph Problem, " Comm. Math. Univ. Carol. 26 (1985), 415--419.

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