On the Complexity of Optimal Drawings of Graphs

We consider the problem of producing aesthetically nice drawings of graphs from the complexity point of view. The following questions are immediate: (1) How to formalize in algorithmic terms that a drawing is nice? (2) What are the computational costs for nice drawings? (3) Are there tools to beat the NP-completeness?

[1]  David S. Johnson.  The NP-Completeness Column: An Ongoing Guide , 1986, J. Algorithms.

[2]  Franz-Josef Brandenburg,et al.  Nice drawings of graphs are computationally hard , 1988, Informatics and Psychology Workshop.

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Michael J. Fischer,et al.  Optimal tree layout (Preliminary Version) , 1980, STOC '80.

[5]  Grzegorz Rozenberg,et al.  Boundary NLC Graph Grammars-Basic Definitions, Normal Forms, and Complexity , 1986, Inf. Control..

[6]  Leslie G. Valiant,et al.  Universality considerations in VLSI circuits , 1981, IEEE Transactions on Computers.

[7]  Manfred Nagl,et al.  Graph-Grammars and Their Application to Computer Science , 1986, Lecture Notes in Computer Science.

[8]  Jeffrey D Ullma.  Computational Aspects of VLSI , 1984 .

[9]  James B. Orlin,et al.  NP-Completeness for Minimizing Maximum Edge Length in Grid Embeddings , 1985, J. Algorithms.

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

[11]  Angelo Gregori,et al.  Unit-Length Embedding of Binary Trees on a Square Grid , 1989, Inf. Process. Lett..

[12]  Roberto Tamassia,et al.  On Embedding a Graph in the Grid with the Minimum Number of Bends , 1987, SIAM J. Comput..

[13]  D. Dolev,et al.  Planar Embedding of Planar Graphs , 1983 .

[14]  Franz-Josef Brandenburg,et al.  On Polynomial Time Graph Grammars , 1988, STACS.

[15]  A. O. Slisenko.  Context-Free Grammars as a Tool for Describing Polynomial-Time Subclasses of Hard Problems , 1982, Inf. Process. Lett..

[16]  Bruno Courcelle.  An Axiomatic Definition of Context-Free Rewriting and its Application to NLC Graph Grammars , 1987, Theor. Comput. Sci..

[17]  Joost Engelfriet,et al.  Boundary Graph Grammars with Dynamic Edge Relabeling , 1990, J. Comput. Syst. Sci..

[18]  Edward M. Reingold,et al.  Tidier Drawings of Trees , 1981, IEEE Transactions on Software Engineering.

[19]  Stavros S. Cosmadakis,et al.  The Complexity of Minimizing Wire Lengths in VLSI Layouts , 1987, Inf. Process. Lett..

[20]  Grzegorz Rozenberg,et al.  On the structure of node-label-controlled graph languages , 1980, Inf. Sci..

[21]  James A. Storer,et al.  On minimal-node-cost planar embeddings , 1984, Networks.