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Feedback vertex set

About: Feedback vertex set is a(n) research topic. Over the lifetime, 2205 publication(s) have been published within this topic receiving 49218 citation(s). more


Journal ArticleDOI: 10.1137/0611030
Abstract: The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is, shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorith... more

Topics: Vertex (graph theory) (67%), Laplacian matrix (64%), Neighbourhood (graph theory) (64%) more

1,706 Citations

Journal ArticleDOI: 10.1287/OPRE.16.5.955
Michael B. Teitz1, Polly Bart1Institutions (1)
Abstract: The generalized vertex median of a weighted graph may be found by complete enumeration or by some heuristic method. This paper investigates alternatives and proposes a method that seems to perform well in comparison with others found in the literature. more

Topics: Vertex (graph theory) (68%), Feedback vertex set (63%), Simplex graph (62%) more

767 Citations

Open accessJournal ArticleDOI: 10.1016/0304-3975(94)00097-3
Rodney G. Downey1, Michael R. Fellows2Institutions (2)
Abstract: For many fixed-parameter problems that are trivially solvable in polynomial-time, such as k -DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as FEEDBACK VERTEX SET, exhibit fixed-parameter tractability : for each fixed k the problem is solvable in time bounded by a polynomial of degree c , where c is a constant independent of k . In a previous paper, the W Hierarchy of parameterized problems was defined, and complete problems were identified for the classes W [ t ] for t ⩾ 2. Our main result shows that INDEPENDENT SET is complete for W [1]. more

Topics: Feedback vertex set (57%), Dominating set (57%), Completeness (order theory) (55%) more

617 Citations

Journal ArticleDOI: 10.1109/TAC.2005.861710
Yoonsoo Kim1, Mehran Mesbahi2Institutions (2)
Abstract: We consider the set G consisting of graphs of fixed order and weighted edges. The vertex set of graphs in G will correspond to point masses and the weight for an edge between two vertices is a functional of the distance between them. We pose the problem of finding the best vertex positional configuration in the presence of an additional proximity constraint, in the sense that, the second smallest eigenvalue of the corresponding graph Laplacian is maximized. In many recent applications of algebraic graph theory in systems and control, the second smallest eigenvalue of Laplacian has emerged as a critical parameter that influences the stability and robustness properties of dynamic systems that operate over an information network. Our motivation in the present work is to "assign" this Laplacian eigenvalue when relative positions of various elements dictate the interconnection of the underlying weighted graph. In this venue, one would then be able to "synthesize" information graphs that have desirable system theoretic properties. more

Topics: Algebraic connectivity (71%), Laplacian matrix (68%), Resistance distance (66%) more

564 Citations

Journal ArticleDOI: 10.1016/0165-0114(87)90114-X
Weimin Dong1, Haresh C. Shah1Institutions (1)
Abstract: This paper is to introduce a new approach — the vertex method — for computing functions of fuzzy variables. The method is based on the α-cut concept and interval analysis. The vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi-occurrence of variables in the functional expression by conventional interval analysis methods. The algorithm is very easy to implement and can be applied to many practical problems. Some examples are given to illustrate the applications. more

Topics: Feedback vertex set (59%), Fuzzy number (58%), Fuzzy set (57%) more

521 Citations

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Topic's top 5 most impactful authors

Saket Saurabh

91 papers, 1.8K citations

Daniel Lokshtanov

62 papers, 1.4K citations

Fedor V. Fomin

36 papers, 1.2K citations

Daniël Paulusma

26 papers, 217 citations

Venkatesh Raman

26 papers, 454 citations

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