A branch-and-cut approach to the crossing number problem

Buchheim, Christoph; Chimani, Markus; Ebner, Dietmar; Gutwenger, Carsten; Jünger, Michael; Klau, Gunnar W.; Mutzel, Petra; Weiskircher, René

doi:10.1016/j.disopt.2007.05.006

Cited by 26 publications

(38 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Buchheim et al [5] presented an integer linear programming (ILP) formulation of the crossing minimization problem and demonstrated how to solve it to optimality with a Branch-and-Cut approach. This approach was made more practical for medium sized graphs by the introduction of a combinatorial column generation scheme by Chimani et al [7].…”

Section: Exact Crossing Minimizationmentioning

confidence: 99%

“…We will only briefly sketch the ILP approach mentioned above; for details see [5]. The conceptual idea is to have a variablex e, f for each pair of edges which is 1 if the two edges cross, and 0 otherwise.…”

Section: Exact Crossing Minimizationmentioning

confidence: 99%

“…The Kuratowski-constraints used in [5] force at least one crossing on each such substructure. We do not need to modify these constraints nor their separation for usage in SCM + .…”

Section: Exact Crossing Minimizationmentioning

confidence: 99%

See 2 more Smart Citations

Crossing Minimization meets Simultaneous Drawing

Chimani

Jünger

Schulz

2008

2008 IEEE Pacific Visualization Symposium

Self Cite

View full text Add to dashboard Cite

We define the concept of crossing numbers for simultaneous graphs by extending the crossing number problem of traditional graphs. We discuss differences to the traditional crossing number problem, and give an NP-completeness proof and lower and upper bounds for the new problem. Furthermore, we show how existing heuristic and exact algorithms for the traditional problem can be adapted to the new task of simultaneous crossing minimization, and report on a brief experimental study of their implementations.

show abstract

Section: Exact Crossing Minimizationmentioning

confidence: 99%

Section: Exact Crossing Minimizationmentioning

confidence: 99%

See 1 more Smart Citation

Crossing Minimization meets Simultaneous Drawing

Chimani

Jünger

Schulz

2008

2008 IEEE Pacific Visualization Symposium

Self Cite

View full text Add to dashboard Cite

show abstract

“…These findings have made the area of crossing minimization one of the most active research topics in the graph drawing community; see [3] for an excellent survey. However, the problem of crossing minimization is computationally hard [9], and it remains hard even when restricted to special graphs [12].…”

Section: Related Workmentioning

confidence: 99%

“…Given that the problem is difficult, several heuristics have been designed. The heuristics are usually hard to implement and they do not scale well with the size of a graph [3]. Hence, it is a reasonable question to ask to what extent one should try to minimize edge crossings to justify the cost.…”

Section: Related Workmentioning

confidence: 99%

Are Crossings Important for Drawing Large Graphs?

Kobourov

Pupyrev

Saket

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Reducing the number of edge crossings is considered one of the most important graph drawing aesthetics. While real-world graphs tend to be large and dense, most of the earlier work on evaluating the impact of edge crossings utilizes relatively small graphs that are manually generated and manipulated. We study the effect on task performance of increased edge crossings in automatically generated layouts for graphs, from different datasets, with different sizes, and with different densities. The results indicate that increasing the number of crossings negatively impacts accuracy and performance time and that impact is significant for small graphs but not significant for large graphs. We also quantitatively evaluate the impact of edge crossings on crossing angles and stress in automatically constructed graph layouts. We find a moderate correlation between minimizing stress and the minimizing the number of crossings.

show abstract