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arXiv · 1706.10228

Contracting a Planar Graph Efficiently

Jacob Holm·Giuseppe F. Italiano·Adam Karczmarz·Jakub Łącki·Eva Rotenberg·Piotr Sankowski
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Abstract

We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report all the arising self-loops and parallel edges. By applying the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar graph problems, including decremental 2-vertex and 3-edge connectivity, and we show that using our data structure in a black-box manner, one obtains conceptually simple optimal algorithms for computing MST and 5-coloring in planar graphs.

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Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Łącki, Eva Rotenberg, Piotr Sankowski. 2017-06-30. Contracting a Planar Graph Efficiently. https://arxiv.org/abs/1706.10228

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