Topological morphing of planar graphs

In this paper we study how two planar embeddings of the same biconnected graph can be morphed one into the other while minimizing the number of elementary changes.

[1]  Raymond Lister,et al.  Sorting Circular Permutations by Reversal. , 2003, WADS.

[2]  Jan Kratochvíl,et al.  Testing planarity of partially embedded graphs , 2010, SODA '10.

[3]  Anna Lubiw,et al.  Morphing orthogonal planar graph drawings , 2013, SODA '06.

[4]  Stephen G. Kobourov,et al.  Intersection-Free Morphing of Planar Graphs , 2003, GD.

[5]  Roberto Tamassia,et al.  On-Line Planarity Testing , 1989, SIAM J. Comput..

[6]  Shimon Even,et al.  Graph Algorithms , 1979 .

[7]  Therese C. Biedl,et al.  Morphing Planar Graphs While Preserving Edge Directions , 2005, GD.

[8]  David Sankoff,et al.  Exact and Approximation Algorithms for the Inversion Distance Between Two Chromosomes , 1993, CPM.

[9]  Anna Lubiw,et al.  Morphing Planar Graph Drawings , 2007, CCCG.

[10]  Anne Bergeron,et al.  Advances on sorting by reversals , 2007, Discret. Appl. Math..

[11]  Ioannis G. Tollis,et al.  Graph Drawing , 1994, Lecture Notes in Computer Science.

[12]  Alberto Caprara,et al.  Sorting by reversals is difficult , 1997, RECOMB '97.

[13]  Vineet Bafna,et al.  Genome rearrangements and sorting by reversals , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[14]  Giuseppe Di Battista,et al.  Finding a Minimum-depth Embedding of a Planar Graph in O(n4) Time , 2009, Algorithmica.

[15]  Robert E. Tarjan,et al.  Dividing a Graph into Triconnected Components , 1973, SIAM J. Comput..

[16]  David A. Bader,et al.  A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study , 2001, J. Comput. Biol..

[17]  Craig Gotsman,et al.  Guaranteed intersection-free polygon morphing , 2001, Comput. Graph..

[18]  David Sankoff,et al.  Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement , 1995, Algorithmica.

[19]  Christian Bachmaier,et al.  Track Planarity Testing and Embedding ? , 2004 .

[20]  Carsten Thomassen,et al.  Deformations of plane graphs , 1983, J. Comb. Theory, Ser. B.

[21]  Peter van Emde Boas,et al.  SOFSEM 2004: Theory and Practice of Computer Science , 2004, Lecture Notes in Computer Science.

[22]  Niklaus Wirth,et al.  Algorithms and Data Structures , 1989, Lecture Notes in Computer Science.

[23]  Clyde L. Monma,et al.  On the complexity of embedding planar graphs to minimize certain distance measures , 2005, Algorithmica.

[24]  C. Gotsman,et al.  How to morph tilings injectively , 1999 .

[25]  Haim Kaplan,et al.  Faster and simpler algorithm for sorting signed permutations by reversals , 1997, SODA '97.

[26]  Frank Kammer,et al.  Determining the Smallest k Such That G Is k -Outerplanar , 2007, ESA.

[27]  S. S. Cairns.  Deformations of Plane Rectilinear Complexes , 1944 .

[28]  Maria Emilia M. T. Walter,et al.  Reversal Distance of Signed Circular Chromosomes , 2000 .

[29]  Ajith Abraham,et al.  Estimating genome reversal distance by genetic algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[30]  Walter Didimo,et al.  Computing Orthogonal Drawings with the Minimum Number of Bends , 1997, IEEE Trans. Computers.