A tighter insertion-based approximation of the crossing number
نویسندگان
چکیده
منابع مشابه
A Tighter Insertion-Based Approximation of the Crossing Number
Let G be a planar graph and F a set of additional edges not yet in G. The multiple edge insertion problem (MEI) asks for a drawing of G+F with the minimum number of pairwise edge crossings, such that the subdrawing of G is plane. As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor (depending ...
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We show that, if P6=NP, there is a constant c0 > 1 such that there is no c0approximation algorithm for the crossing number, even when restricted to 3-regular graphs.
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We prove that the crossing number of an apex graph, i.e. a graph G from which only one vertex v has to be removed to make it planar, can be approximated up to a factor of ∆(G−v)·d(v)/2 by solving the vertex inserting problem, i.e. inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Since the latter problem can be solved in polynomial time, this es...
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Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straightline drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can cross. The tangle crossing number of a tangl...
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The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a well-known open question on crossing numbe...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2016
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-016-0030-z