• Corpus ID: 7249609

# Packing Cycles Faster Than Erd\H{o}s-P\'osa

@article{Lokshtanov2017PackingCF,
title={Packing Cycles Faster Than Erd\H\{o\}s-P\'osa},
author={Daniel Lokshtanov and Amer E. Mouawad and Saket Saurabh and Meirav Zehavi},
journal={arXiv: Data Structures and Algorithms},
year={2017}
}
• Published 4 July 2017
• Computer Science
• arXiv: Data Structures and Algorithms
The Cycle Packing problem asks whether a given undirected graph $G=(V,E)$ contains $k$ vertex-disjoint cycles. Since the publication of the classic Erd\H{o}s-P\'osa theorem in 1965, this problem received significant scientific attention in the fields of Graph Theory and Algorithm Design. In particular, this problem is one of the first problems studied in the framework of Parameterized Complexity. The non-uniform fixed-parameter tractability of Cycle Packing follows from the Robertson-Seymour…

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It is shown that the undirected edge-disjoint cycle packing problem is quasi-NP-hard to approximate within ratio of $O(\log^{\frac{1}{2}-\epsilon}n)$ for any constant ε>0.
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It is shown that the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like Cycle Packing, and in several cases it is able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail.