Fixed-parameter algorithms for vertex cover P3

Let Pℓ denote a path in a graph G=(V,E) with ℓ vertices. A vertex coverPℓsetC in G is a vertex subset such that every Pℓ in G has at least a vertex in C. The Vertex CoverPℓ problem is to find a vertex cover Pℓ set of minimum cardinality in a given graph. This problem is NP-hard for any integer ℓ⩾2....

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Veröffentlicht in:Discrete optimization Jg. 19; S. 12 - 22
Hauptverfasser: Chang, Maw-Shang, Chen, Li-Hsuan, Hung, Ling-Ju, Rossmanith, Peter, Su, Ping-Chen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.02.2016
Schlagworte:
Bounded-degree-1 set
Branch and reduce
Fixed-parameter algorithm
Vertex cover [formula omitted]
Branch and reduce
Vertex cover P3
Bounded-degree-1 set
Fixed-parameter algorithm
ISSN:1572-5286, 1873-636X
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Zusammenfassung:Let Pℓ denote a path in a graph G=(V,E) with ℓ vertices. A vertex coverPℓsetC in G is a vertex subset such that every Pℓ in G has at least a vertex in C. The Vertex CoverPℓ problem is to find a vertex cover Pℓ set of minimum cardinality in a given graph. This problem is NP-hard for any integer ℓ⩾2. The parameterized version of Vertex CoverPℓ problem called k-Vertex CoverPℓ asks whether there exists a vertex cover Pℓ set of size at most k in the input graph. In this paper, we give two fixed parameter algorithms to solve the k-Vertex CoverP3 problem. The first algorithm runs in time O∗(1.7964k) in polynomial space and the second algorithm runs in time O∗(1.7485k) in exponential space. Both algorithms are faster than previous known fixed-parameter algorithms.
ISSN:1572-5286
1873-636X
DOI:10.1016/j.disopt.2015.11.003