A Linear Algorithm for Finding a Maximal Planar Subgraph
نویسنده
چکیده
We construct an optimal linear time algorithm for the maximal planar subgraph problem: given a graph G, nd a planar subgraph G 0 of G such that adding to G 0 any edge of G not present in G 0 leads to a non-planar graph. Our solution is based on a dynamic graph search procedure and a fast data structure for on-line planarity testing of triconnected graphs. Our algorithm can be transformed into a new optimal planarity testing algorithm.
منابع مشابه
A Linear-Time Algorithm for Finding a Maximal Planar Subgraph
We construct an optimal linear-time algorithm for the maximal planar subgraph problem: given a graph G, find a planar subgraph G′ of G such that adding to G′ an extra edge of G results in a non-planar graph. Our solution is based on a fast data structure for incremental planarity testing of triconnected graphs and a dynamic graph search procedure. Our algorithm can be transformed into a new opt...
متن کاملA Linear Time Algorithm for Finding a Maximal Planar Subgraph Based on PC-Trees
In Shih & Hsu, a planarity test was introduced utilizing a data structure called PC-trees, generalized from PQ-trees. They illustrated that a PC-tree is more natural IN representing planar graphs. Their algorithm starts by constructing a depth-first-search tree and adds all back edges to a vertex one by one. A major feature in the S&H algorithm is that, at each iteration, at most two terminal n...
متن کاملA Mathematical Modeling for Plastic Analysis of Planar Frames by Linear Programming and Genetic Algorithm
In this paper, a mathematical modeling is developed for plastic analysis of planar frames. To this end, the researcher tried to design an optimization model in linear format in order to solve large scale samples. The computational result of CPU time requirement is shown for different samples to prove efficiency of this method for large scale models. The fundamental concept of this model is ob...
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 کاملAn O(m log n)-Time Algorithm for the Maximal Planar Subgraph Problem
Based on a new version of Hopcroft and Tarjan’s planarity testing algorithm, we develop an O (mlogn)-time algorithm to find a maximal planar subgraph.
متن کامل