A New Approximation Algorithm for Finding Heavy Planar Subgraphs (1997)
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| Venue: | ALGORITHMICA |
| Citations: | 7 - 1 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.
