## A Polynomial Time Randomized Parallel Approximation Algorithm for Finding Heavy Planar Subgraphs (2006)

### BibTeX

@MISC{Osipov06apolynomial,

author = {Vitaly Osipov},

title = {A Polynomial Time Randomized Parallel Approximation Algorithm for Finding Heavy Planar Subgraphs},

year = {2006}

}

### OpenURL

### Abstract

We provide an approximation algorithm for the Maximum Weight Planar Subgraph problem, the NP-hard problem of finding a heaviest planar subgraph in an edge-weighted graph G. In the general case our algorithm has performance ratio at least 1/3 + 1/72 matching the best algorithm known so far, though in several special cases we prove stronger results. In particular, we obtain performance ratio 2/3 (instead of 7/12) for the NP-hard Maximum Weight Outerplanar Subgraph problem meeting the performance ratio of the best algorithm for the unweighted case. When the maximum weight planar subgraph is one of several special types of Hamiltonian graphs, we show performance ratios at least 2/5 and 4/9 (instead of 1/3 + 1/72), and 1/2 (instead of 4/9) for the unweighted case.