## A New Approximation Algorithm for Finding Heavy Planar Subgraphs (1997)

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Venue: | ALGORITHMICA |

Citations: | 8 - 2 self |

### BibTeX

@ARTICLE{Calinescu97anew,

author = {Gruia Calinescu and Cristina G. Fernandes and Howard Karloff and Alexander Zelikovsky},

title = {A New Approximation Algorithm for Finding Heavy Planar Subgraphs},

journal = {ALGORITHMICA},

year = {1997},

volume = {36},

pages = {2003}

}

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### Abstract

We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NP-Hard problem of finding a heaviest planar subgraph in an edge-weighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had performance ratio exceeding 1=3, which is obtained by any algorithm that produces a maximum weight spanning tree in G. Based on the Berman-Ramaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3 + 1/72. We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8. Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2) for the NP-Hard MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.