--- res: bibo_abstract: - 'We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding '' : G ! M of a graph G into a 2manifold M maps the vertices in V (G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to a common node or arc, due to data compression or low resolution. This raises the computational problem of deciding whether a given map '' : G ! M comes from an embedding. A map '' : G ! M is a weak embedding if it can be perturbed into an embedding ψ: G ! M with k'' "k < " for every " > 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl [14], which reduces to solving a system of linear equations over Z2. It runs in O(n2!) O(n4:75) time, where 2:373 is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler than [14]: We perform a sequence of local operations that gradually "untangles" the image ''(G) into an embedding (G), or reports that '' is not a weak embedding. It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon [1], and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Hugo foaf_name: Akitaya, Hugo foaf_surname: Akitaya - foaf_Person: foaf_givenName: Radoslav foaf_name: Fulek, Radoslav foaf_surname: Fulek foaf_workInfoHomepage: http://www.librecat.org/personId=39F3FFE4-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-8485-1774 - foaf_Person: foaf_givenName: Csaba foaf_name: Tóth, Csaba foaf_surname: Tóth bibo_doi: 10.1137/1.9781611975031.20 dct_date: 2018^xs_gYear dct_identifier: - UT:000483921200021 dct_language: eng dct_publisher: ACM@ dct_title: Recognizing weak embeddings of graphs@ ...