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Randomized parameterized algorithms for \(P_2\)-Packing and Co-Path Packing problems

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Abstract

In this paper, we study the Parameterized \(P_2\)-Packing problem and Parameterized Co-Path Packing problem from random perspective. For the Parameterized \(P_2\)-Packing problem, based on the structure analysis of the problem and using random partition technique, a randomized parameterized algorithm of running time \(O^*(6.75^k)\) is obtained, improving the current best result \(O^*(8^k)\). For the Parameterized Co-Path Packing problem, we firstly study the kernel and randomized algorithm for the degree-bounded instance, where each vertex in the instance has degree at most three. A kernel of size \(20k\) and a randomized algorithm of running time \(O^*(2^k)\) are given for the Parameterized Co-Path Packing problem with bounded degree constraint. By applying iterative compression technique and based on the randomized algorithm for degree bounded problem, a randomized algorithm of running time \(O^*(3^k)\) is given for the Parameterized Co-Path Packing problem.

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Notes

  1. Following a recent convention, for a function \(f\), we will use the notion \(O^*(f)\) for the bound \(O(f \! \cdot \! n^{O(1)})\).

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant (61232001, 61103033, 61173051, 61370172).

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha , 410083, People’s Republic of China

    Qilong Feng, Jianxin Wang, Shaohua Li & Jianer Chen

  2. Department of Computer Science, Texas A&M University, College Station, TX, USA

    Jianer Chen

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  1. Qilong Feng
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  2. Jianxin Wang
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  3. Shaohua Li
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  4. Jianer Chen
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Corresponding author

Correspondence to Jianxin Wang.

Additional information

A preliminary version of this work was reported in the Proceedings of the 19th Annual International Computing and Combinatorics Conference, Lecture Notes in Computer Science, vol. 7936, 2013, pp. 89–100.

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Feng, Q., Wang, J., Li, S. et al. Randomized parameterized algorithms for \(P_2\)-Packing and Co-Path Packing problems. J Comb Optim 29, 125–140 (2015). https://doi.org/10.1007/s10878-013-9691-z

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  • DOI: https://doi.org/10.1007/s10878-013-9691-z

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