The Maximum Acyclic Subgraph Problem and Degree-3 Graphs

Authors:
Alantha Newman
Affiliations:
-
Venue:
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Year:
2001

Citing 2
Cited 0

Tight bounds for the maximum acyclic subgraph problem

Journal of Algorithms
Fences Are Futile: On Relaxations for the Linear Ordering Problem

Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the problem of finding a maximum acyclic subgraph of a given directed graph in which the maximum total degree (in plus out) is 3. For these graphs, we present: (i) a simple combinatorial algorithm that achieves an 11/12-approximation (the previous best factor was 2/3 [1]), (ii) a lower bound of 125/126 on approximability, and (iii) an approximation-preserving reduction from the general case: if for any Ɛ 0, there exists a (17/18 + Ɛ)-approximation algorithm for the maximum acyclic subgraph problem in graphs with maximum degree 3, then there is a (1/2+δ)-approximation algorithm for general graphs for some δ 0. The problem of finding a better-than-half approximation for general graphs is open.