article

Breaking cycles for minimizing crossings

Authors:

Camil Demestrescu,

Irene FinocchiAuthors Info & Claims

Journal of Experimental Algorithmics (JEA), Volume 6

Pages 2 - es

https://doi.org/10.1145/945394.945396

Published: 31 December 2001 Publication History

Abstract

We consider the one-sided crossing minimization problem (CP): given a bipartite graph G and a permutation x₀ of the vertices on a layer, find a perumuation x₁ of the vertices on the other layer which minimizes the number of edge crossings in any straightline drawing of G where vertices are placed on two parallel lines and sorted according to x₀ and x₁. Solving CP represents a fundamental step in the construction of aesthetically pleasing layouts of heirarchies and directed graphs, but unfortunately this problem has been proved to be NP-complete.

In this paper we address the strong relation between CP and the problem of computing minimum feedback arc sets in directed graphs and we devise a enw approximation algorithm for CP, called PM, that exploits this dependency. We experimantally and visually compare the performance of PM with the performance of well-known algorithms and of recent attractive strategies. Experiments are carried out on different families of randomly generated graphs, on pathological instances, and on real test sets. Performance indicators include both number of edge crossings and running time, as well as structural measures of the problem instances. We found CP to be a very interesting and rich problem from a combinatorial point of view. Our results clearly separate the behavior of the algorithms, proving the effectiveness of PM on most test sets and showing tradeoffs between quality of the solutions and running time. However, if the visual complexity of the drawings is considered, we found no clear winner. This confirms the importance of optimizing also other aesthetic criteria such as symmetry, edge length, and angular resolution.

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Cited By

Baumann JRutter ISudholt DLi XHandl J(2024)Evolutionary Computation Meets Graph Drawing: Runtime Analysis for Crossing Minimisation on Layered Graph DrawingsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654105(1533-1541)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654105
Ahmed RAngelini PBekos MBattista GKaufmann MKindermann PKobourov SNöllenburg MSymvonis AVilledieu AWallinger M(2023)Splitting Vertices in 2-Layer Graph DrawingsIEEE Computer Graphics and Applications10.1109/MCG.2023.326424443:3(24-35)Online publication date: 1-May-2023
https://doi.org/10.1109/MCG.2023.3264244
Faralli SFinocchi IPonzetto SVelardi P(2018)Efficient pruning of large knowledge graphsProceedings of the 27th International Joint Conference on Artificial Intelligence10.5555/3304222.3304334(4055-4063)Online publication date: 13-Jul-2018
https://dl.acm.org/doi/10.5555/3304222.3304334
Show More Cited By

Index Terms

Breaking cycles for minimizing crossings
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Paths and connectivity problems
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Journal of Experimental Algorithmics

ACM Journal of Experimental Algorithmics Volume 6, Issue

2001

313 pages

ISSN:1084-6654

EISSN:1084-6654

DOI:10.1145/945394

Issue’s Table of Contents

Copyright © 2001 ACM.

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Association for Computing Machinery

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Publication History

Published: 31 December 2001

Published in JEA Volume 6

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Cited By

Baumann JRutter ISudholt DLi XHandl J(2024)Evolutionary Computation Meets Graph Drawing: Runtime Analysis for Crossing Minimisation on Layered Graph DrawingsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654105(1533-1541)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654105
Ahmed RAngelini PBekos MBattista GKaufmann MKindermann PKobourov SNöllenburg MSymvonis AVilledieu AWallinger M(2023)Splitting Vertices in 2-Layer Graph DrawingsIEEE Computer Graphics and Applications10.1109/MCG.2023.326424443:3(24-35)Online publication date: 1-May-2023
https://doi.org/10.1109/MCG.2023.3264244
Faralli SFinocchi IPonzetto SVelardi P(2018)Efficient pruning of large knowledge graphsProceedings of the 27th International Joint Conference on Artificial Intelligence10.5555/3304222.3304334(4055-4063)Online publication date: 13-Jul-2018
https://dl.acm.org/doi/10.5555/3304222.3304334
Khan SBilal MSharif MKhan F(2011)A solution to bipartite drawing problem using genetic algorithmProceedings of the Second international conference on Advances in swarm intelligence - Volume Part I10.5555/2026282.2026355(530-538)Online publication date: 12-Jun-2011
https://dl.acm.org/doi/10.5555/2026282.2026355
Harrigan MHealy P(2011)k-level crossing minimization is NP-hard for treesProceedings of the 5th international conference on WALCOM: algorithms and computation10.5555/1966169.1966181(70-76)Online publication date: 18-Feb-2011
https://dl.acm.org/doi/10.5555/1966169.1966181
Khan SBilal MSharif MKhan F(2011)A Solution to Bipartite Drawing Problem Using Genetic AlgorithmAdvances in Swarm Intelligence10.1007/978-3-642-21515-5_63(530-538)Online publication date: 2011
https://doi.org/10.1007/978-3-642-21515-5_63
Harrigan MHealy P(2011)k-Level Crossing Minimization Is NP-Hard for TreesWALCOM: Algorithms and Computation10.1007/978-3-642-19094-0_9(70-76)Online publication date: 2011
https://doi.org/10.1007/978-3-642-19094-0_9
Çakıroglu OErten CKarataş ÖSözdinler M(2009)Crossing minimization in weighted bipartite graphsJournal of Discrete Algorithms10.1016/j.jda.2008.08.0037:4(439-452)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.1016/j.jda.2008.08.003
Çakiroğlu OErten CKaratas ÖSözdinler M(2007)Crossing minimization in weighted bipartite graphsProceedings of the 6th international conference on Experimental algorithms10.5555/1768570.1768584(122-135)Online publication date: 6-Jun-2007
https://dl.acm.org/doi/10.5555/1768570.1768584
Çakıroḡlu OErten CKarataş ÖSözdinler M(2007)Crossing Minimization in Weighted Bipartite GraphsExperimental Algorithms10.1007/978-3-540-72845-0_10(122-135)Online publication date: 2007
https://doi.org/10.1007/978-3-540-72845-0_10
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