We present space-efficient algorithms for computing cut vertices in a given graph with n vertices and m edges in linear time using O(n+min{m,n log log n}) bits. With the same time and using O(n+m) bits, we can compute the biconnected components of a graph. We use this result to show an algorithm for the recognition of (maximal) outerplanar graphs in O(n log log n) time using O(n) bits.
@InProceedings{kammer_et_al:LIPIcs.MFCS.2016.56, author = {Kammer, Frank and Kratsch, Dieter and Laudahn, Moritz}, title = {{Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs}}, booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)}, pages = {56:1--56:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-016-3}, ISSN = {1868-8969}, year = {2016}, volume = {58}, editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.56}, URN = {urn:nbn:de:0030-drops-64683}, doi = {10.4230/LIPIcs.MFCS.2016.56}, annote = {Keywords: graph algorithms, space efficiency, cut vertices, maximal outerplanar graphs} }
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