2002/07/24 by David Eppstein, Eppstein, David · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #DNA and Biological Computing #Data Structures and Algorithms (cs.DS) #F.2.2 #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.cs/0207082
13 pages, 2 figures
arxiv created 2002/07/24 · openalex publication_date 2002/07/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time O(log n + log g(log log g)3) per update on a surface of genus g; we can also test orientability of the surface in the same time, and maintain the minimum and maximum spanning tree of the graph in time O(log n + log4 g) per update. Our data structure allows edge insertion and deletion as well as the dual operations; these operations may implicitly change the genus of the embedding surface. We apply similar ideas to improve the constant factor in a separator theorem for low-genus graphs, and to find in linear time a tree-decomposition of low-genus low-diameter graphs.