Results 1 
7 of
7
Planarizing Graphs  A Survey and Annotated Bibliography
, 1999
"... Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results abo ..."
Abstract

Cited by 32 (0 self)
 Add to MetaCart
Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results about vertex splitting, thickness, and crossing number are mostly of a structural nature. We also include a brief section on vertex deletion. We do not consider parallel algorithms, nor do we deal with online algorithms.
Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
 ALGORITHMICA
, 1996
"... ..."
Solving the Maximum Weight Planar Subgraph Problem by Branch and Cut
 PROCEEDINGS OF THE THIRD CONFERENCE ON INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION
, 1993
"... In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3 ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3;3 , turn out to define facets of this polytope. We also present computational experience with a branch and cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K 5 or K 3;3 . These structures give us inequalities which are used as cutting planes.
Graph Planarization and Skewness
"... The problem of finding a maximum spanning planar subgraph of a nonplanar graph is NPComplete. Several heuristics for the problem have been devised but their worstcase performance is unknown, although a trivial lower bound of 1/3 the optimum number of edges is easily shown. We discuss a new heurist ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
The problem of finding a maximum spanning planar subgraph of a nonplanar graph is NPComplete. Several heuristics for the problem have been devised but their worstcase performance is unknown, although a trivial lower bound of 1/3 the optimum number of edges is easily shown. We discuss a new heuristic, based on spanning trees, for generating a subgraph with size at least 2/3 of the optimum for any input graph. The skewness of the ndimensional hypercube Qn is also derived. Finally, we explore the relationship between the skewness and crossing number of a graph.
An improved convex optimization model for twodimensional facility layout
, 2006
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public.
Graph Planarization
, 1998
"... . We survey graph planarization and related problems. We first describe variants and applications of graph planarization. Then we focus on algorithms. We begin by describing the branchandcut algorithm of Junger and Mutzel (1996). Then, we review work on heuristics based on planarity testing an ..."
Abstract
 Add to MetaCart
. We survey graph planarization and related problems. We first describe variants and applications of graph planarization. Then we focus on algorithms. We begin by describing the branchandcut algorithm of Junger and Mutzel (1996). Then, we review work on heuristics based on planarity testing and those based on twophase procedures. Finally, computational results comparing algorithms for graph planarization are presented. 1. Introduction A graph is said to be planar if it can be drawn on the plane in such a way that no two of its edges cross. Given a graph G = (V, E) with vertex set V and edge set E, the objective of graph planarization is to find a minimum cardinality subset of edges F # E such that the graph G # = (V, E \ F ), resulting from the removal of the edges in F from G, is planar. This problem is also known as the maximum planar subgraph problem. A related and simpler problem is that of finding a maximal planar subgraph, which is a planar subgraph G # = (V, E # ) ...
Graph Theoretic Based Heuristics For the Facility Layout Design Problems
"... The facility layout problem is concerned with determining the location of a number of facilities which optimizes a prescribed objective such as profit, cost, or distance. This problem arises in many applications; for example, in design of buildings and in plant layout design. The facility layout pro ..."
Abstract
 Add to MetaCart
The facility layout problem is concerned with determining the location of a number of facilities which optimizes a prescribed objective such as profit, cost, or distance. This problem arises in many applications; for example, in design of buildings and in plant layout design. The facility layout problem has been modeled as: a quadratic assignment problem; a quadratic set covering problem; a linear integer programming problem; a graph theoretic problem. Since this problem is NPcomplete, most approaches are heuristic in nature and based on graph theoretic concepts. Graph theoretically, when the objective is to maximize profit, the facility layout problem is to determine, in a given edge weighted graph G, a maximum weight planar subgraph. In this paper, we discuss a number of heuristics for this problem. The performance of the heuristics is established through a comparative analysis based on an extensive set of random test problems. 1. Introduction Typically the facility layout design ...