An Experimental Study of Crossing Minimization Heuristics

Gutwenger, Carsten; Mutzel, Petra

doi:10.1007/978-3-540-24595-7_2

Cited by 34 publications

(40 citation statements)

References 27 publications

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“…For the computation of heuristic values we used the planarization approach. Gutwenger and Mutzel presented an extensive computational study of crossing minimization heuristics [9]. The authors investigate the effects of various methods for the computation of a maximal planar subgraph and different edge re-insertion strategies for the planarization approach.…”

Section: Computational Resultsmentioning

confidence: 99%

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Exact Crossing Minimization

et al. 2006

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Abstract. The crossing number of a graph is the minimum number of edge crossings in any drawing of the graph into the plane. This very basic property has been studied extensively in the literature from a theoretic point of view and many bounds exist for a variety of graph classes. In this paper, we present the first algorithm able to compute the crossing number of general sparse graphs of moderate size and present computational results on a popular benchmark set of graphs. The approach uses a new integer linear programming formulation of the problem combined with strong heuristics and problem reduction techniques. This enables us to compute the crossing number for 91 percent of all graphs on up to 40 nodes in the benchmark set within a time limit of five minutes per graph.

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Section: Computational Resultsmentioning

confidence: 99%

“…Pre-and post-processing procedures have been developed to improve the solution quality. A computational study on state-of-the-art heuristics can be found in [9].…”

Section: Introductionmentioning

confidence: 99%

Exact Crossing Minimization

et al. 2006

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“…In crossing minimization, the problem is to find a drawing with the minimum number of crossings. The problem is NP-Complete [8] but there has been a great deal of research on heuristic algorithms [9]. Graph planarization [13] is often used together with careful reinsertion of edges.…”

Section: Related Workmentioning

confidence: 99%

An Interactive Multi-user System for Simultaneous Graph Drawing

Kobourov

Pitta

2005

Graph Drawing

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Abstract. In this paper we consider the problem of simultaneous drawing of two graphs. The goal is to produce aesthetically pleasing drawings for the two graphs by means of a heuristic algorithm and with human assistance. Our implementation uses the DiamondTouch table, a multiuser, touch-sensitive input device, to take advantage of direct physical interaction of several users working collaboratively. The system can be downloaded at http://dt.cs.arizona.edu where it is also available as an applet.

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“…Later, and rather surprisingly, it was shown in [14] that there exists a linear-time algorithm, using the SPQR-tree datastructure, which finds the optimal insertion path for e over all possible planar embeddings of H. In [13] it was shown that this approach is in practice vastly superior to the former in terms of the overall obtained number of crossings.…”

Section: Introductionmentioning

confidence: 99%

Advances in the Planarization Method: Effective Multiple Edge Insertions

Chimani¹,

Gutwenger

2012

Graph Drawing

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Abstract. The planarization method is the strongest known method to heuristically find good solutions to the general crossing number problem in graphs: starting from a planar subgraph, one iteratively inserts edges, representing crossings via dummy nodes. In the recent years, several improvements both from the practical and the theoretical point of view have been made. We review these advances and conduct an extensive study of the algorithms' practical implications. Thereby, we present the first implementation of an approximation algorithm for the crossing number problem of general graphs, and compare the obtained results with known exact crossing number solutions.

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An Experimental Study of Crossing Minimization Heuristics

Cited by 34 publications

References 27 publications

Exact Crossing Minimization

Exact Crossing Minimization

An Interactive Multi-user System for Simultaneous Graph Drawing

Advances in the Planarization Method: Effective Multiple Edge Insertions

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