Lempel, Even, and Cederbaum Planarity Method
نویسندگان
چکیده
We present a simple pedagogical graph theoretical description of Lempel, Even, and Cederbaum (LEC) planarity method based on concepts due to Thomas. A linear-time implementation of LEC method using the PC-tree data structure of Shih and Hsu is provided and described in details. We report on an experimental study involving this implementation and other available linear-time implementations of planarity algorithms.
منابع مشابه
Planarity Testing and Embedding
Universita’ di Roma Tre 3.1 Properties and Characterizations of Planar Graphs . . . . . 2 Basic Definitions • Properties • Characterizations 3.2 Planarity Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 History of Planarity Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.4 Common Algorithmic Techniques and Tools . . . . . ...
متن کاملAlgorithms for Testing and Embedding Planar Graphs
2 Embedding graphs into planarity 3 2.1 embedding algorithms donot use PQ-trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 A planarity embedding algorithm based on the Kuratowski theorem . . . . . . . . 3 2.1.2 An embedding algorithm based on open ear decomposition . . . . . . . . . . . . . . 3 2.1.3 A simplified o (n) planar embedding algorithm for biconnected graphs . . ....
متن کاملOn the Cutting Edge: Simplified O(n) Planarity by Edge Addition
We present new O(n)-time methods for planar embedding and Kuratowski subgraph isolation that were inspired by the Booth-Lueker PQ-tree implementation of the Lempel-Even-Cederbaum vertex addition method. In this paper, we improve upon our conference proceedings formulation and upon the Shih-Hsu PC-tree, both of which perform comprehensive tests of planarity conditions embedding the edges from a ...
متن کاملA Linear Algorithm for Embedding Planar Graphs Using PQ-Trees
This paper presents a simple linear algorithm for embedding (or drawing) a planar graph in the plane. The algorithm is based on the “vertex-addition” algorithm of Lempel, Even, and Cederbaum (“Theory of Graphs,” Intl. Sympos. Rome, July 1966, pp. 21>232, Gordon & Breach, New York, 1967) for the planarity testing, and is a modification of Booth and Lueker’s (J. Comput. System Sci. 13 (1976), 335...
متن کاملA Linear Time Algorithm For Finding Maximal Planar Subgraphs
Given an undirected graph G, the maximal planar subgraph problem is to determine a planar subgraph H of G such that no edge of G-H can be added to H without destroying planarity. Polynomial algorithms have been obtained by Jakayumar, Thulasiraman and Swamy [6] and Wu [9]. O(mlogn) algorithms were previously given by Di Battista and Tamassia [3] and Cai, Han and Tarjan [2]. A recent O(m α α (n))...
متن کامل