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A Mixed-Integer Program for Drawing Orthogonal Hyperedges in a Hierarchical Hypergraph

Author

Listed:
  • Gregory Fridman

    (Department of Applied Mathematics and Mathematical Methods in Economics, Saint Petersburg State University of Economics, Griboedov Canal Emb., 30-32, 191023 St. Petersburg, Russia)

  • Yuri Vasiliev

    (Department of Applied Mathematics and Mathematical Methods in Economics, Saint Petersburg State University of Economics, Griboedov Canal Emb., 30-32, 191023 St. Petersburg, Russia)

  • Vlada Puhkalo

    (Department of Applied Mathematics and Mathematical Methods in Economics, Saint Petersburg State University of Economics, Griboedov Canal Emb., 30-32, 191023 St. Petersburg, Russia)

  • Vladimir Ryzhov

    (Department of Applied Mathematics and Mathematical Modeling, Saint Petersburg State Marine Technical University, Lotsmanskaya Ulitsa, 3, 190121 St. Petersburg, Russia)

Abstract

This paper presents a new formulation and solution of a mixed-integer program for the hierarchical orthogonal hypergraph drawing problem, and the number of hyperedge crossings is minimized. The novel feature of the model is in combining several stages of the Sugiyama framework for graph drawing: vertex ordering, the assignment of vertices’ x -coordinates, and orthogonal hyperedge routing. The hyperedges of a hypergraph are assumed to be multi-source and multi-target, and vertices are depicted as rectangles with ports on their top and bottom sides. Such hypergraphs are used in data-flow diagrams and in a scheme of cooperation. The numerical results demonstrate the correctness and effectiveness of the proposed approach compared to mathematical heuristics. For instance, the proposed exact approach yields a 67.3 % reduction of the number of crossings compared to that obtained by using a mathematical heuristic for a dataset of non-planar graphs.

Suggested Citation

  • Gregory Fridman & Yuri Vasiliev & Vlada Puhkalo & Vladimir Ryzhov, 2022. "A Mixed-Integer Program for Drawing Orthogonal Hyperedges in a Hierarchical Hypergraph," Mathematics, MDPI, vol. 10(5), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:689-:d:756428
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    Citations

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    Cited by:

    1. Jana Fortes & Michal Staš, 2023. "Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs," Mathematics, MDPI, vol. 11(13), pages 1-10, July.

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