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- W2953105898 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2011 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)On Graph Crossing Number and Edge PlanarizationJulia Chuzhoy, Yury Makarychev, and Anastasios SidiropoulosJulia Chuzhoy, Yury Makarychev, and Anastasios Sidiropoulospp.1050 - 1069Chapter DOI:https://doi.org/10.1137/1.9781611973082.80PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their endpoints. A crossing in such a drawing is a point where two such curves intersect. In the Minimum Crossing Number problem, the goal is to find a drawing of G with minimum number of crossings. The value of the optimal solution, denoted by OPT, is called the graph's crossing number. This is a very basic problem in topological graph theory, that has received a significant amount of attention, but is still poorly understood algorithmically. The best currently known efficient algorithm produces drawings with O(log2 n). (n + OPT) crossings on bounded-degree graphs, while only a constant factor hardness of approximation is known. A closely related problem is Minimum Planarization, in which the goal is to remove a minimum-cardinality subset of edges from G, such that the remaining graph is planar. Our main technical result establishes the following connection between the two problems: if we are given a solution of cost k to the Minimum Planarization problem on graph G, then we can efficiently find a drawing of G with at most poly(d) · k · (k + OPT) crossings, where d is the maximum degree in G. This result implies an O(n · poly(d) · log3/2 n)-approximation for Minimum Crossing Number, as well as improved algorithms for special cases of the problem, such as, for example, k-apex and bounded-genus graphs. Previous chapter Next chapter RelatedDetails Published:2011ISBN:978-0-89871-993-2eISBN:978-1-61197-308-2 https://doi.org/10.1137/1.9781611973082Book Series Name:ProceedingsBook Code:PR138Book Pages:xviii-1788" @default.
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- W2953105898 date "2011-01-23" @default.
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- W2953105898 title "On Graph Crossing Number and Edge Planarization" @default.
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