Abstract
We study the problem of finding a maximum acyclic subgraph of a given directed graph in which the maximum total degree (inplus 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 ε > 0, there exists a (17/18 + ε)-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.
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References
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Newman, A. (2001). The Maximum Acyclic Subgraph Problem and Degree-3 Graphs. In: Goemans, M., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. RANDOM APPROX 2001 2001. Lecture Notes in Computer Science, vol 2129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44666-4_18
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DOI: https://doi.org/10.1007/3-540-44666-4_18
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