Exact computation of minimum feedback vertex sets with relational algebra

Authors:
Rudolf Berghammer;Alexander Fronk
Affiliations:
Institute of Computer Science and Applied Mathematics, University of Kiel, Kiel, Germany;Software Technology, University of Dortmund, Dortmund, Germany
Venue:
Fundamenta Informaticae
Year:
2005

Citing 8
Cited 5

Circuits, handles, bridges and nets

APN 90 Proceedings on Advances in Petri nets 1990
Relations and graphs: discrete mathematics for computer scientists

Relations and graphs: discrete mathematics for computer scientists
Free choice Petri nets

Free choice Petri nets
Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference

SIAM Journal on Computing
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem

SIAM Journal on Discrete Mathematics
Approximating Minimum Feedback Sets and Multi-Cuts in Directed Graphs

Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
Implementation of Relational Algebra Using Binary Decision Diagrams

ReIMICS '01 Revised Papers from the 6th International Conference and 1st Workshop of COST Action 274 TARSKI on Relational Methods in Computer Science
Using Relation Algebra for the Analysis of Petri Nets in a CASE Tool Based Approach

SEFM '04 Proceedings of the Software Engineering and Formal Methods, Second International Conference

State space analysis of Petri nets with relation-algebraic methods

Journal of Symbolic Computation
On relational cycles

RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
Solving algorithmic problems on orders and lattices by relation algebra and RELVIEW

CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Social software for coalition formation

TARSKI'02-05 Proceedings of the 2006 international conference on Theory and Applications of Relational Structures as Knowledge Instruments - Volume 2
Computing argumentation in polynomial number of BDD operations: a preliminary report

ArgMAS'10 Proceedings of the 7th international conference on Argumentation in Multi-Agent Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

A feedback vertex set of a graph is a subset of vertices containing at least one vertex from every cycle of the graph. Given a directed graph by its adjacency relation, we develop a relational algorithm for computing a feedback vertex set of minimum size. In combination with a BDD-implementation of relations, it allows to exactly solve this NP-hard problem for medium-sized graphs.