@inproceedings{cf5dc58e89d34e00b3d56123e9293f64,
title = "Contracting a planar graph efficiently",
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.",
keywords = "Algorithms, Coloring, Connectivity, Data structures, Planar graphs",
author = "Jacob Holm and Italiano, {Giuseppe F.} and Adam Karczmarz and Jakub {\L}acki and Eva Rotenberg and Piotr Sankowski",
year = "2017",
month = sep,
day = "1",
doi = "10.4230/LIPIcs.ESA.2017.50",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Christian Sohler and Christian Sohler and Kirk Pruhs",
booktitle = "25th European Symposium on Algorithms, ESA 2017",
note = "25th European Symposium on Algorithms, ESA 2017 ; Conference date: 04-09-2017 Through 06-09-2017",
}