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The main result is a new succinct encoding achieving the information-theory optimal bound of 3.24 bits per vertex, while allowing efficient navigation. Our representation is based on the bijection of Poulalhon and Schaeffer (Algorithmica, 46(3):505\u2013527, 2006) that defines a mapping between planar triangulations and a special class of spanning trees, called <jats:italic>PS-trees<\/jats:italic>. The proposed solution differs from previous approaches in that operations in planar triangulations are reduced to operations in particular <jats:italic>parentheses sequences<\/jats:italic> encoding PS-trees. Existing methods to handle balanced parentheses sequences have to be combined and extended to operate on such specific sequences, essentially for retrieving matching elements. The new encoding supports extracting the <jats:italic>d<\/jats:italic> neighbors of a query vertex in <jats:italic>O<\/jats:italic>(<jats:italic>d<\/jats:italic>) time and testing adjacency between two vertices in <jats:italic>O<\/jats:italic>(1) time. Additionally, we provide an implementation of our proposed data structure. In the experimental evaluation, our representation reaches up to 7.35 bits per vertex, improving the space usage of state-of-the-art implementations for planar embeddings.<\/jats:p>","DOI":"10.1007\/s00453-021-00861-4","type":"journal-article","created":{"date-parts":[[2021,8,9]],"date-time":"2021-08-09T02:02:26Z","timestamp":1628474546000},"page":"3432-3468","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Succinct Encoding of Binary Strings Representing Triangulations"],"prefix":"10.1007","volume":"83","author":[{"given":"Jos\u00e9","family":"Fuentes-Sep\u00falveda","sequence":"first","affiliation":[]},{"given":"Diego","family":"Seco","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5484-9104","authenticated-orcid":false,"given":"Raquel","family":"Via\u00f1a","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,9]]},"reference":[{"key":"861_CR1","doi-asserted-by":"crossref","unstructured":"Aleardi, L.C., Devillers, O., Rossignac, J.: ESQ: editable squad representation for triangle meshes. 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