Journal ArticleDOI
The assignment heuristic for crossing reduction
Tiziana Catarci
- Vol. 25, Iss: 3, pp 515-521
TLDR
A heuristic is presented for edge crossing minimization in bipartite graphs, which works by reducing the problem to an assignment problem, and it is shown that the idea underlying the assignment heuristic can be effectively applied in other cases requiring edge crossings minimization.Abstract:
Several applications use algorithms for drawing k-layered networks and, in particular, 2-layered networks (i.e. bipartite graphs). Bipartite graphs are commonly drawn in the plane so that all vertices lie on two parallel vertical lines, and an important requirement in drawing such graphs is to minimize edge crossings. Such a problem is NP-complete even when the position of the vertices on one layer is held fixed. This paper presents a heuristic, called the assignment heuristic, for edge crossing minimization in bipartite graphs, which works by reducing the problem to an assignment problem. The main idea of the assignment heuristic is to position simultaneously all the vertices of one layer, so that the mutual interaction of the position of all the vertices can be taken into account. We also show that the idea underlying the assignment heuristic can be effectively applied in other cases requiring edge crossing minimization. >read more
Citations
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Journal ArticleDOI
Grasp and Path Relinking for 2-Layer Straight Line Crossing Minimization
Manuel Laguna,Rafael Martí +1 more
TL;DR: A greedy randomized adaptive search procedure (GRASP) for the problem of minimizing straight line crossings in a 2-layer graph is developed and indicates that graph density is a major influential factor on the performance of a solution procedure.
Journal ArticleDOI
2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms
Michael Jünger,Petra Mutzel +1 more
TL;DR: It is concluded that there is no need for heuristics if one layer is xed, even though the problem is NP-hard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes.
Journal ArticleDOI
On Bipartite Drawings and the Linear Arrangement Problem
TL;DR: The bipartite crossing number problem is studied and a connection between this problem and the linear arrangement problem is established, and a lower bound and an upper bound for the optimal number of crossings are derived, where the main terms are the optimal arrangement values.
Journal ArticleDOI
Track layouts of graphs
Sue Whitesides,Vida Dujmović +1 more
TL;DR: This thesis introduces and comprehensively study so-called track layouts of graphs and their subdivisions, and establishes that graphs of bounded treewidth have three-dimensional straight-line grid drawings with linear volume.
Proceedings Article
Hierarchical Drawing Algorithms.
Patrick Healy,Nikola S. Nikolov +1 more
TL;DR: The University of Limerick 17.17.2018, Limerick, Ireland as discussed by the authors, Dublin, Ireland, United Kingdom, Ireland.Reference as discussed by the authors : http://www.universityof-limerick.edu.
References
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Journal ArticleDOI
The Hungarian method for the assignment problem
TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.
Book
Flows in networks
D. R. Ford,D. R. Fulkerson +1 more
TL;DR: Ford and Fulkerson as mentioned in this paper set the foundation for the study of network flow problems and developed powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
Journal ArticleDOI
Flows in Networks.
TL;DR: The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.