Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
The Programming Language Aspects of ThingLab, a Constraint-Oriented Simulation Laboratory
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Detection, prevention and recovery from deadlocks in multiprocess multiple resource systems
Detection, prevention and recovery from deadlocks in multiprocess multiple resource systems
An axiomatic approach to control description and implementation
An axiomatic approach to control description and implementation
ACM Transactions on Mathematical Software (TOMS)
New bounds on the size of the minimum feedback vertex set in meshes and butterflies
Information Processing Letters
Minimum feedback vertex sets in shuffle-based interconnection networks
Information Processing Letters
Feedback vertex sets in star graphs
Information Processing Letters
New upper bounds on feedback vertex numbers in butterflies
Information Processing Letters
A constraint programming approach to cutset problems
Computers and Operations Research
Feedback arc set in bipartite tournaments is NP-complete
Information Processing Letters
Feedback vertex sets in mesh-based networks
Theoretical Computer Science
Feedback numbers of de Bruijn digraphs
Computers & Mathematics with Applications
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The problem of finding a minimum cardinality feedback vertex set of a directed graph is considered. Of the classic NP-complete problems, this is one of the least understood. Although Karp showed the general problem to be NP-complete, a linear algorithm for its solution on reducible flow graphs was given by Shamir. The class of reducible flow graphs is the only nontrivial class of graphs for which a polynomial-time algorithm to solve this problem is known. The main result of this paper is to present a new class of graphs—the cyclically reducible graphs—for which minimum feedback vertex sets can be found in polynomial time. This class is not restricted to flow graphs, and most small graphs (10 or fewer nodes) fall into this class. The identification of this class is particularly important since there do not exist approximation algorithms for this problem having a provably good worst case performance. Along with the class and a simple polynomial-time algorithm for finding minimum feedback vertex sets of graphs in the class, several related results are presented. It is shown that there is no “forbidden subgraph” characterization of the class and that there is no particular inclusion relationship between this class and the reducible flow graphs. In addition, it is shown that a class of (general) graphs, which are related to the reducible flow graphs, are contained in the cyclically reducible class.