SIAM Journal on Computing
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Faster and simpler algorithm for sorting signed permutations by reversals
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Computing Orthogonal Drawings with the Minimum Number of Bends
IEEE Transactions on Computers
Graph Algorithms
Exact and Approximation Algorithms for the Inversion Distance Between Two Chromosomes
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
Morphing orthogonal planar graph drawings
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Advances on sorting by reversals
Discrete Applied Mathematics
Genome rearrangements and sorting by reversals
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Determining the smallest k such that G is k-outerplanar
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Testing planarity of partially embedded graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Morphing planar graphs while preserving edge directions
GD'05 Proceedings of the 13th international conference on Graph Drawing
Journal of Discrete Algorithms
h-quasi planar drawings of bounded treewidth graphs in linear area
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
| Hi-index | 5.23 |
In this paper we analyze the relationships among different planar embeddings of the same graph and study how two planar embeddings can be morphed one into the other with the minimum number of elementary changes, while preserving the mental map of the user. We call this problem Topological Morphing, in analogy with the well-known Geometric Morphing problem, in which it is studied how two planar drawings can be morphed one into the other with the minimum number of elementary changes. First, we define two operations, called flip and skip, describing natural transformations of a graph embedding that preserve the mental map of the user. Then, we study the problem of performing a morph while minimizing the number of these operations. We show that the Topological Morphing problem is NP-hard for biconnected planar graphs, we give polynomial-time algorithms for some restricted versions of the problem, and, based on such polynomial-time algorithms, we give a fixed-parameter tractable algorithm for the general case.