Cooperation scheme visualization: coordinate assignment

Abstract

Purpose: the author considers the problem of assigning coordinates to the vertices at hierarchical graph placement for 2D drawing. Discussion: сoordinate assignment is the stage of the Sugiyama method for drawing directed acyclic hierarchical graph following the edge crossing minimization stage. The solution of the problem is 2D coordinates of each vertex, taking into account the fixed order of vertices on each layer. Results: the author discussed and mathematically formalized the set of aesthetic drawing criteria. The author confirmed the exact mathematical statement of the problem in the form of mixed-integer programming. Numerical evaluation demonstrates effectiveness and correctness of the proposed approach.