• The Transactions of the Korean Institute of Electrical Engineers P
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• v.53 no.4
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• pp.210-215
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• 2004

This paper proposes an implicit method for computing the minimum cost feedback vertex set for a graph. For an arbitrary graph, a Boolean function is derived, whose satisfying assignments directly correspond to feedback vertex sets of the graph. Importantly, cycles in the graph are never explicitly enumerated, but rather, are captured implicitly in this Boolean function. This function is then used to determine the minimum cost feedback vertex set. Even though computing the minimum cost satisfying assignment for a Boolean function remains an NP-hard problem, it is possible to exploit the advances made in the area of Boolean function representation in logic synthesis to tackle this problem efficiently in practice for even reasonably large sized graphs. The algorithm has obvious application in flip-flop selection for partial scan. The algorithm proposed in this paper is the first to obtain the MFVS solutions for many benchmark circuits.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.11-20
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• 1995

A new graph problem is formulated to limit the maximum path length of a general directed graph when a minimal set of vertices together with their incident edges are removed from the graph. An optimal algorithm and a heuristic algorithm are proposed and the proposed heuristic algorithm is shown to be effective through experiments using a collection of graphs obtained from large sequential circuits. The heuristic algorithm is based on a feedback vertex set algorithm based on graph reduction.