## An Analysis of Heuristics for Graph Planarization (1997)

Venue: | Journal of Information & Optimization Sciences |

Citations: | 3 - 0 self |

### BibTeX

@ARTICLE{Cimikowski97ananalysis,

author = {Robert Cimikowski},

title = {An Analysis of Heuristics for Graph Planarization},

journal = {Journal of Information & Optimization Sciences},

year = {1997},

volume = {18},

pages = {49--73}

}

### OpenURL

### Abstract

We analyze several heuristics for graph planarization, i.e., deleting the minimum number of edges from a nonplanar graph to make it planar. The problem is NP-hard, although some heuristics which perform well in practice have been reported. In particular, we compare the two principle methods, based on path addition and vertex addition, respectively, with a selective edge addition method, an incremental method, and a "cycle packing" approach. For the incremental, the path addition, and the edge addition methods, we prove theoretical worst-case performance bounds of 1=3. We also present an empirical analysis of the heuristics. Our results indicate that the "cycle-packing" method consistently yields the best solutions when applied to a large set of test graphs. 1

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Citation Context ... selective edge addition heuristic CHT , the incremental method INC, and a "cycle packing" method GT . We describe the other heuristics briefly now. 4.1 The Vertex-Addition Heuristic Booth a=-=nd Lueker [2] developed-=- a planarity algorithm based on vertex addition. The algorithm embeds one vertex of a graph at each step in the order given by a special numbering of the vertices called an "st-numbering." O... |

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Citation Context ...heuristics. A number of heuristics for the problem have appeared in the form of algorithms for finding a maximal planar subgraph of a nonplanar graph, for example [4, 5, 11, 12, 16] and more recently =-=[8]-=- in this journal. However, it is shown in [3] that there are graphs for which the ratio between the sizes of any two maximal planar subgraphs can be as small as 1=3. Hence, unless some precautions are... |

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Citation Context ...g an edge if it causes nonplanarity. The remaining edges form a maximal planar subgraph. After each edge addition, a planarity test is performed. Using an "incremental" planarity testing met=-=hod, e.g. [13]-=-, the time complexity is O(n + mff(m; n)) (also see [6, 20]). (ff(m; n) is the functional inverse of Ackermann's function, and is less than 4 for all practical values of m and n). 3.3.1 Worst-Case Ana... |