Tight Localizations of Feedback Sets

01/06/2020
by   Michael Hecht, et al.
0

The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs ε⊆ E or vertices ν⊆ V whose removal G∖ε, G∖ν makes a given multi-digraph G=(V,E) acyclic, respectively. The corresponding decision problems are part of the 21 NP-complete problems of R. M. Karp's famous list. Though both problems are known to be APX-hard, approximation algorithms or proofs of inapproximability are unknown. We propose a new O(|V||E|^4)-heuristic for the directed FASP. While r ≈ 1.3606 is known to be a lower bound for the APX-hardness, at least by validation, we show that r ≤ 2. Applying the approximation preserving L-reduction from the directed FVSP to the FASP thereby allows computing feedback vertex sets with the same accuracy. Benchmarking the algorithm with state of the art alternatives yields that, for the first time, the most relevant instance class of large sparse graphs can be solved efficiently within tight error bounds. Our derived insights might provide a path to prove the APX-completeness of both problems.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/26/2023

PACE Solver Description: A Heuristic Directed Feedback Vertex Set Problem Algorithm

A feedback vertex set of a graph is a set of nodes with the property tha...
research
12/12/2022

Degreewidth: a New Parameter for Solving Problems on Tournaments

In the paper, we define a new parameter for tournaments called degreewid...
research
01/02/2022

Classifying Subset Feedback Vertex Set for H-Free Graphs

In the Feedback Vertex Set problem, we aim to find a small set S of vert...
research
07/02/2017

Dynamic Parameterized Problems and Algorithms

Fixed-parameter algorithms and kernelization are two powerful methods to...
research
02/18/2018

Minimum length RNA folding trajectories

The Kinfold and KFOLD programs for RNA folding kinetics implement the Gi...
research
09/06/2018

Min (A)cyclic Feedback Vertex Sets and Min Ones Monotone 3-SAT

In directed graphs, we investigate the problems of finding: 1) a minimum...
research
03/30/2021

Determining a Slater Winner is Complete for Parallel Access to NP

We consider the complexity of deciding the winner of an election under t...

Please sign up or login with your details

Forgot password? Click here to reset