Journal of Combinatorial Optimization

, Volume 32, Issue 2, pp 594–607 | Cite as

An \(O^{*}(1.4366^n)\)-time exact algorithm for maximum \(P_2\)-packing in cubic graphs

  • Maw-Shang Chang
  • Li-Hsuan Chen
  • Ling-Ju Hung


Given a graph \(G=(V, E)\), a \(P_2\)-packing \(\mathcal {P}\) is a collection of vertex disjoint copies of \(P_2\)s in \(G\) where a \(P_2\) is a simple path with three vertices and two edges. The Maximum \(P_2\)-Packing problem is to find a \(P_2\)-packing \(\mathcal {P}\) in the input graph \(G\) of maximum cardinality. This problem is NP-hard for cubic graphs. In this paper, we give a branch-and-reduce algorithm for the Maximum \(P_2\)-Packing problem in cubic graphs. We analyze the running time of the algorithm using measure-and-conquer and show that it runs in time \(O^{*}(1.4366^n)\) which is faster than previous known exact algorithms where \(n\) is the number of vertices in the input graph.


\(P_2\)-packing Cubic graphs Branch-and-reduce algorithms  Measure-and-conquer 



This research is partially supported by the Ministry of Science and Technology of Taiwan under Grants NSC 101–2221–E–241–019–MY3 and NSC 102–2221–E–241–007–MY3. Ling-Ju Hung (corresponding author) is supported by the Ministry of Science and Technology of Taiwan under Grant NSC 103–2811–E–241–001.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringHungKuang UniversityTaichungTaiwan
  2. 2.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan

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