Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
One Sided Crossing Minimization Is NP-Hard for Sparse Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
An Improved Bound on the One-Sided Minimum Crossing Number in Two-Layered Drawings
Discrete & Computational Geometry
On the one-sided crossing minimization in a bipartite graph with large degrees
Theoretical Computer Science
Fixed parameter algorithms for one-sided crossing minimization revisited
Journal of Discrete Algorithms
Aggregating inconsistent information: Ranking and clustering
Journal of the ACM (JACM)
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Ranking and drawing in subexponential time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
A Note on Exact Algorithms for Vertex Ordering Problems on Graphs
Theory of Computing Systems
Parameterized Complexity
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We give a subexponential fixed parameter algorithm for one-sided crossing minimization. It runs in $O(3^{\sqrt{2k}} + n)$ time, where n is the number of vertices of the given graph and parameter k is the number of crossings. The exponent of $O(\sqrt{k})$ in this bound is asymptotically optimal assuming the Exponential Time Hypothesis and the previously best known algorithm runs in $2^{O(\sqrt{k}\log k)} + n^{O(1)}$ time. We achieve this significant improvement by the use of a certain interval graph naturally associated with the problem instance and a simple dynamic program on this interval graph. The linear dependency on n is also achieved through the use of this interval graph.