Mathematical Programming Formulation of Rectilinear Crossing Minimization
نویسنده
چکیده
In a rectilinear drawing of a simple graph G each vertex is mapped to a distinct point in the plane and each edge is represented by a straight-line segment with appropriate ends. The goal of rectilinear crossing minimization is to find a rectilinear drawing of G with as few edge crossings as possible. A new approach to rectilinear crossing minimization is presented including a formulation of the problem as a mathematical program with a linear objective function and simple quadratic constraints. Then we size the problem for various graph families. These sizings provide a mechanism for ranking crossing number problems according to their apparent complexity.
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