# Exact Localisations of Feedback Sets

@article{Hecht2017ExactLO, title={Exact Localisations of Feedback Sets}, author={Michael Hecht}, journal={Theory of Computing Systems}, year={2017}, volume={62}, pages={1048-1084} }

The feedback arc (vertex) set problem, shortened FASP (FVSP), is to transform a given multi digraph G = (V, E) into an acyclic graph by deleting as few arcs (vertices) as possible. Due to the results of Richard M. Karp in 1972 it is one of the classic NP-complete problems. An important contribution of this paper is that the subgraphs Gel(e), Gsi(e) of all elementary cycles or simple cycles running through some arc e β E, can be computed in π|E|2$\mathcal {O}\big (|E|^{2}\big )$ and π(|E|4β¦Β

## 5 Citations

### Tight Localizations of Feedback Sets

- Computer Science, MathematicsACM J. Exp. Algorithmics
- 2021

This work proposes a new universal O(|V||E|4)βheuristic for the directed FASP and achieves an approximation of r β€ 2.6 within tight error bounds with this approach.

### An Exact Method for the Minimum Feedback Arc Set Problem

- MathematicsACM J. Exp. Algorithmics
- 2021

An exact method is proposed for sparse graphs that enumerates simple cycles in a lazy fashion and iteratively extends an incomplete cycle matrix and the practical limits of the new method are evaluated on a test set containing computationally challenging sparse graphs, relevant for industrial applications.

### Generalized Layerings for Arbitrary and Fixed Drawing Areas

- Computer ScienceJ. Graph Algorithms Appl.
- 2017

This work presents the Generalized Layering Problem (GLP), which solves the combination of DLP and FASP simultaneously, allowing general graphs as input and observes that GLP reduces the number of dummy nodes significantly, can produce more compact drawings, and improves on graphs where DLP yields poor aspect ratios.

### Biggs Theorem for Directed Cycles and Topological Invariants of Digraphs

- Mathematics, Computer ScienceAdvances in Pure Mathematics
- 2021

It is proved the computation of the 2nd Betti number to be sharp #P hard in general and specific representation invariant sub-fillings yielding efficiently computable homology groups.

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