An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
Given a graph G = (V,E), the task in the vertex cover P3(V C P3) problem is to find a minimum subset of vertices F ⊆ V such that every path of order 3 in G contains at least one vertex from F. The V C P3problem remains NP-hard even in planar graphs and has many applications in real world. In this pa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2019-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2060 |
| Summary: | Given a graph G = (V,E), the task in the vertex cover P3(V C P3) problem is to find a minimum subset of vertices F ⊆ V such that every path of order 3 in G contains at least one vertex from F. The V C P3problem remains NP-hard even in planar graphs and has many applications in real world. In this paper, we give a dynamic-programming algorithm to solve the V C P3problem on graphs of bounded branchwidth. Using the dynamic programming algorithm and the Baker’s EPTAS framework for NP-hard problems, we present an efficient polynomial time approximation scheme (EPTAS) for the V C P3problem on planar graphs. |
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| ISSN: | 2083-5892 |