The vertex separation number of a graph equals its path-width
Information Processing Letters
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
Algorithms for area-efficient orthogonal drawings
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Optimal three-dimensional orthogonal graph drawing in the general position model
Theoretical Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Clean the graph before you draw it!
Information Processing Letters
Balanced vertex-orderings of graphs
Discrete Applied Mathematics
Cutwidth II: Algorithms for partial w-trees of bounded degree
Journal of Algorithms
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
On the complexity of the balanced vertex ordering problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Parameterized Complexity
| Hi-index | 0.89 |
In the Imbalance Minimization problem we are given a graph G=(V,E) and an integer b and asked whether there is an ordering v"1...v"n of V such that the sum of the imbalance of all the vertices is at most b. The imbalance of a vertex v"i is the absolute value of the difference between the number of neighbors to the left and right of v"i. The problem is also known as the Balanced Vertex Ordering problem and it finds many applications in graph drawing. We show that this problem is fixed parameter tractable and provide an algorithm that runs in time 2^O^(^b^l^o^g^b^)@?n^O^(^1^). This resolves an open problem of Kara et al. [On the complexity of the balanced vertex ordering problem, in: COCOON, in: Lecture Notes in Comput. Sci., vol. 3595, 2005, pp. 849-858].