D. J. Brown, M. R. Fellows and M. A. Langston, "Polynomial-Time Self-Reducibility: Theoretical Motivations and Practical Results," Int'l J. of Computer Mathematics 31 (1989), 1--9.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....journals and conferences. Then we present algorithms which improve and unify previous results. Algorithms for subgraph isomorphism can be classified in terms of a series of successively stronger problems: ffl Existential algorithms answer the question Does G contain a subgraph isomorphic to H [3]. ffl Constructive algorithms return a labeled set of k vertices from G which contain a subgraph isomorphic to H, if one exists [10] ffl Enumerative algorithms return a count of how many subgraphs of G are isomorphic to H [6] ffl Enumeration algorithms return all labeled sets of k vertices ....

....k vertices from G which contain a subgraph isomorphic 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 ....

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D. J. Brown, M. R. Fellows, and M. Langston. Polynomial-time self reducibility: Theoretical motivations and practical results. Int. J. Computer Math, 31:1--9, 1989.

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D. J. Brown, M. R. Fellows and M. A. Langston, "Polynomial-Time Self-Reducibility: Theoretical Motivations and Practical Results," Int'l J. of Computer Mathematics 31 (1989), 1--9.

....the corresponding search problem S , any method that isolates a solution to S by repeated calls to an algorithm that answers D is commonly termed a self reduction. Although we have previously identified straightforward self reduction methods that can be applied to many layout permutation problems [BFL, FL4], we herein develop considerably more efficient search strategies. To accomplish this, we introduce a general technique that we call sca olding, and show how it can be the basis for fast search algorithms for a number of layout permutation problems, including MIN CUT LINEAR ARRANGEMENT, GATE ....

....[MaS] where n denotes the number of vertices in G. Thus MIN CUT LINEAR ARRANGEMENT is in P for any fixed value of k. We have shown [FL4] however, that the asymptotic time complexity can be reduced to O(n 2 ) for any fixed k. This can be used to obtain an O(n 4 ) search strategy. Theorem 1. [BFL] For any fixed k, a satisfactory solution to MINCUT LINEAR ARRANGEMENT can be constructed, if any exist, by an oracle algorithm (with overhead O(n 2 ) that makes O(n 2 ) calls to an O(n 2 ) decision oracle for MIN CUT LINEAR ARRANGEMENT. If, as in Theorem 1, the oracle language consulted by ....

D. J. Brown, M. R. Fellows and M. A. Langston, "Polynomial-Time Self-Reducibility: Theoretical Motivations and Practical Results," Int'l J. of Comp. Math. 31 (1989), 1--9.

....of K 4 , however, merely approximates its cutwidth at three. In particular, such an absence says nothing at all about how to find a layout of width three even if many should exist. To solve this problem, our algorithms can be used in conjunction with previously studied self reduction techniques [BFL, FL2] to search for a layout in O(n 2 ) time. Many other combinatorial problems may benefit from fast immersion tests. For example, a variety of load factor [FL1] problems can be decided by a finite battery of immersion tests, including K 4 . A problem indirectly approachable with this method is ....

D. J. Brown, M. R. Fellows and M. A. Langston, "Polynomial-Time Self-Reducibility: Theoretical Motivations and Practical Results," Int'l J. of Computer Mathematics 31 (1989), 1--9.

No context found.

D. J. Brown, M. R. Fellows and M. A. Langston, "Polynomial-Time Self-Reducibility: Theoretical Motivations and Practical Results," Int'l J. of Computer Mathematics 31 (1989), 1--9.

....address this question here. 6.1 A Self Reduction Technique The term self reduction is used to denote a process that solves the search version of a problem by making repeated calls to an algorithm for the decision version of that problem. Our implementation of the self reduction algorithm from [BFL] uses the procedure FILL IN, which follows. In attempting to change the at most nm 0 s to 1 s, FILL IN makes O(nm) calls to the decision algorithm. When no more changes are possible, a satisfactory column permutation, if one exists, can be found in O(nm) time [BL] We now list the entire layout ....

D. J. Brown, M. R. Fellows, and M. A. Langston, "Polynomial-Time selfreducibility: theoretical motivations and practical results," International Journal of Computer Mathematics 31 (1989), 1--9.

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