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An efficient method for detecting redundant feedback vertices

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  • Berend Hasselman

Abstract

A feedback vertex set of a directed graph cuts all cycles in a directed graph. Such a set can be obtained with the Levy–Low contraction algorithm, which generates a small feedback vertex set but not always a minimum size feedback set since it sometimes needs a heuristic contraction rule in order to reduce a graph completely. This may lead to members in a feedback vertex set being redundant in the sense that they do not cut a cycle of the original directed graph. In this paper we develop two algorithms for detecting such redundant feedback vertices efficiently. The algorithms are applied to analysing large nonlinear normalised systems of equations and to the feedback sets of a series of random directed graphs used by other authors. Computational experiments show that the algorithms developed in this paper significantly improve on the brute force algorithm.

Suggested Citation

  • Berend Hasselman, 2004. "An efficient method for detecting redundant feedback vertices," CPB Discussion Paper 29, CPB Netherlands Bureau for Economic Policy Analysis.
    • Handle: RePEc:cpb:discus:29
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    3. Mr. Hamid Faruqee & Mr. Douglas Laxton & Mr. Bart Turtelboom & Mr. Peter Isard & Mr. Eswar S Prasad, 1998. "Multimod Mark III: The Core Dynamic and Steady State Model," IMF Occasional Papers 1998/010, International Monetary Fund.
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    Cited by:

    1. Olaf van 't Veer, 2006. "Solving large scale normalised rational expectations models," CPB Discussion Paper 54, CPB Netherlands Bureau for Economic Policy Analysis.

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    More about this item

    JEL classification:

    • J51 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Trade Unions: Objectives, Structure, and Effects

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