Randomized parameterized algorithms for $$P_2$$ P 2 -Packing and Co-Path Packing problems

Qilong Feng, Jianxin Wang (), Shaohua Li and Jianer Chen ()
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Qilong Feng: Central South University
Jianxin Wang: Central South University
Shaohua Li: Central South University
Jianer Chen: Central South University

Journal of Combinatorial Optimization, 2015, vol. 29, issue 1, No 7, 125-140

Abstract: Abstract In this paper, we study the Parameterized $$P_2$$ P 2 -Packing problem and Parameterized Co-Path Packing problem from random perspective. For the Parameterized $$P_2$$ P 2 -Packing problem, based on the structure analysis of the problem and using random partition technique, a randomized parameterized algorithm of running time $$O^*(6.75^k)$$ O ∗ ( 6 . 75 k ) is obtained, improving the current best result $$O^*(8^k)$$ 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 $$20k$$ 20 k and a randomized algorithm of running time $$O^*(2^k)$$ 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 $$O^*(3^k)$$ O ∗ ( 3 k ) is given for the Parameterized Co-Path Packing problem.

Keywords: $$P_2$$ P 2 -Packing; Co-Path Packing; Randomized algorithm (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9691-z

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