On-line maintenance of the four-components of a graph (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Constrained visibility representations of graphs
Information Processing Letters
Constructing compact rectilinear planar layouts using canonical representation of planar graphs
Theoretical Computer Science
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A simple linear time algorithm for proper box rectangular drawings of plane graphs
Journal of Algorithms
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
2-Visibility Drawings of Planar Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
Floor-Planning via Orderly Spanning Trees
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Some Applications of Orderly Spanning Trees in Graph Drawing
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Two Algorithms for Finding Rectangular Duals of Planar Graphs
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
A More Compact Visibility Representation
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Improved visibility representation of plane graphs
Computational Geometry: Theory and Applications
New theoretical bounds of visibility representation of plane graphs
GD'04 Proceedings of the 12th international conference on Graph Drawing
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Let G be an n-node planar graph. In a visibility representation of G, each node of G is represented by a horizontal segment such that the segments representing any two adjacent nodes of G are vertically visible to each other. In this paper, we give the best known compact visibility representation of G. Given a canonical ordering of the triangulated G, our algorithm draws the graph incrementally in a greedy manner. We show that one of three canonical orderings obtained from Schnyder's realizer for the triangulated G yields a visibility representation of G no wider than 驴22n-42/15驴. Our easy-to-implement O(n)-time algorithm bypasses the complicated subroutines for four-connected components and four-block trees required by the best previously known algorithm of Kant. Our result provides a negative answer to Kant's open question about whether 驴3n-6/2驴 is a worst-case lower bound on the required width. Moreover, if G has no degree-5 node, then our output for G is no wider than 驴4n-7/3驴. Also, if G is four-connected, then our output for G is no wider than n-1, matching the best known result of Kant and He. As a by-product, we obtain a much simpler proof for a corollary of Wagner's Theorem on realizers, due to Bonichon, Sa毛c, and Mosbah.