Approximating the rectilinear crossing number
نویسندگان
چکیده
منابع مشابه
Approximating the Rectilinear Crossing Number
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straightline segment connecting the corresponding two points. The rectilinear crossing number of a graph G, cr(G), is the minimum number of pairs of crossing edges in any straight-line drawing of G. Determining or estimating cr(G) appears to be a difficult problem, and deciding...
متن کاملApproximating the Maximum Rectilinear Crossing Number
The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...
متن کاملMaximum Rectilinear Crossing Number
The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...
متن کاملApproximating the fixed linear crossing number
We present a randomized polynomial-time approximation algorithm for the fixed linear crossing number problem (FLCNP). In this problem, the vertices of a graph are placed in a fixed order along a horizontal “node line” in the plane, each edge is drawn as an arc in one of the two half-planes (pages), and the objective is to minimize the number of edge crossings. FLCNP is NP-hard, and no previous ...
متن کاملApproximating the Crossing Number of Toroidal Graphs
CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time approximation algorithm is known for this NP-Complete problem. We give in this paper a polynomial time approximation algorithm for the crossing number of toroidal graphs with bounded degree. In course of proving the algorithm we p...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2019
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2019.04.003