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27
An Experimental Comparison of Orthogonal Compaction Algorithms
 In Graph Drawing (Proc. GD 2000
, 2000
"... We present an experimental study in which we compare the stateoftheart methods for compacting orthogonal graph layouts. Given the shape of a planar orthogonal drawing, the task is to place the vertices and the bends on grid points so that the total area or the total edge length is minimised. We c ..."
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Cited by 7 (2 self)
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We present an experimental study in which we compare the stateoftheart methods for compacting orthogonal graph layouts. Given the shape of a planar orthogonal drawing, the task is to place the vertices and the bends on grid points so that the total area or the total edge length is minimised. We compare four constructive heuristics based on rectangular dissection and on turnregularity, also in combination with two improvement heuristics based on longest paths and network flows, and an exact method which is able to compute provable optimal drawings of minimum total edge length. We provide a performance evaluation in terms of quality and running time. The test data consists of two testsuites already used in previous experimental research. In order to get hard instances, we randomly generated an additional set of planar graphs.
Algorithm 797: Fortran Subroutines for Approximate Solution Of . . .
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1999
"... ..."
The Polyhedral Approach to the Maximum Planar Subgraph Problem: New Chances for Related Problems
 In DIMACS Graph Drawing '94, volume 894 of LNCS
, 1994
"... . In [JM94] we used a branch and cut algorithm in order to determine a maximum weight planar subgraph of a given graph. One of the motivations was to produce a nice drawing of a given graph by drawing the found maximum planar subgraph, and then augmenting this drawing by the removed edges. Our exper ..."
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Cited by 3 (2 self)
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. In [JM94] we used a branch and cut algorithm in order to determine a maximum weight planar subgraph of a given graph. One of the motivations was to produce a nice drawing of a given graph by drawing the found maximum planar subgraph, and then augmenting this drawing by the removed edges. Our experiments indicate that drawing algorithms for planar graphs which require 2 or 3connectivity, resp. degreeconstraints, in addition to planarity often give "nicer" results. Thus we are led to the following problems: (1) Find a maximum planar subgraph with maximum degree d 2 IN. (2) Augment a planar graph to a kconnected planar graph. (3) Find a maximum planar kconnected subgraph of a given k connected graph. (4) Given a graph G, which is not necessarily planar and not necessarily kconnected, determine a new graph H by removing r edges and adding a edges such that the new graph H is planar, spanning, kconnected, each node v has degree at most D(v) and r + a is minimum. Problems (1), (2...
Graph Drawing Algorithm Engineering with AGD
, 2000
"... We discuss the algorithm engineering aspects of AGD, a software library of algorithms for graph drawing. AGD represents algorithms as classes that provide one or more methods for calling the algorithm. There is a common base class, also called the type of an algorithm, for algorithms providing basic ..."
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Cited by 3 (2 self)
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We discuss the algorithm engineering aspects of AGD, a software library of algorithms for graph drawing. AGD represents algorithms as classes that provide one or more methods for calling the algorithm. There is a common base class, also called the type of an algorithm, for algorithms providing basically the same functionality. This enables us to exchange components and experiment with various algorithms and implementations of the same type. We give examples for algorithm engineering with AGD for drawing general nonhierarchical graphs and hierarchical graphs.
Approximation algorithms for the Maximum Induced Planar and Outerplanar Subgraph problems
 J. Graph Algorithms Appl
"... The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some new approximation algorithms for MIPS are introduced. The results of an extensive study of the performance of these and exi ..."
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Cited by 2 (1 self)
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The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some new approximation algorithms for MIPS are introduced. The results of an extensive study of the performance of these and existing MIPS approximation algorithms on randomly generated graphs are presented. Efficient algorithms for finding large induced outerplanar graphs are also given. One of these algorithms is shown to find an induced outerplanar subgraph with at least 3n/(d + 5/3) vertices. The results presented in this paper indicate that most existing algorithms perform substantially better than the existing lower bounds indicate. 1
Efficient Extraction of Multiple Kuratowski Subdivisions (TR)
, 2007
"... Abstract. A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for nonplanarity. Modern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is ..."
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Abstract. A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for nonplanarity. Modern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is able to extract multiple Kuratowski subdivisions at once. This is of particular interest for, e.g., BranchandCut algorithms which require multiple such subdivisions to generate cut constraints. The algorithm is not only described theoretically, but we also present an experimental study of its implementation. 1
Apptopinv  user’s guide
, 2003
"... The maximum planar subgraph, maximum outerplanar subgraph, the thickness and outerthickness of a graph are all NPcomplete optimization problems. Apptopinv is a program that contains different heuristic algorithms for these four problems: algorithms based on HopcroftTarjan planarity testing algorit ..."
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Cited by 1 (1 self)
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The maximum planar subgraph, maximum outerplanar subgraph, the thickness and outerthickness of a graph are all NPcomplete optimization problems. Apptopinv is a program that contains different heuristic algorithms for these four problems: algorithms based on HopcroftTarjan planarity testing algorithm, the spanningtree heuristic and various algorithms based on the cactustree heuristic. Apptopinv contains also a simulated annealing algorithm that can be used to improve the solutions obtained from other heuristics. Most of the heuristics have also a greedy version. We have implemented graph generators for complete graphs, complete kpartite graphs, complete hypercubes, random graphs, random maximum planar and outerplanar graphs and random regular graphs. Apptopinv supports three different graph file formats. Apptopinv is written in C++ programming language for Linuxplatform and GCC 2.95.3 compiler. To compile the program, a commercial LEDA algorithm
Two New Approximation Algorithms for the Maximum Planar Subgraph Problem
, 2006
"... The maximum planar subgraph problem (MPS) is defined as follows: given a graph G, find a largest planar subgraph of G. The problem is NPhard and it has applications in graph drawing and resource location optimization. Călinescu et al. [J. Alg. 27, 269302 (1998)] presented the first approximation a ..."
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The maximum planar subgraph problem (MPS) is defined as follows: given a graph G, find a largest planar subgraph of G. The problem is NPhard and it has applications in graph drawing and resource location optimization. Călinescu et al. [J. Alg. 27, 269302 (1998)] presented the first approximation algorithms for MPS with nontrivial performance ratios. Two algorithms were given, a simple algorithm which runs in linear time for boundeddegree graphs with a ratio 7/18 and a more complicated algorithm with a ratio 4/9. Both algorithms produce outerplanar subgraphs. In this article we present two new versions of the simpler algorithm. The first new algorithm still runs in the same time, produces outerplanar subgraphs, has at least the same performance ratio as the original algorithm, but in practice it finds larger planar subgraphs than the original algorithm. The second new algorithm has similar properties to the first algorithm, but it produces only planar subgraphs. We conjecture that the performance ratios of our algorithms are at least 4/9 for MPS. We experimentally compare the new algorithms against the original simple algorithm. We also apply the new algorithms for approximating the thickness and outerthickness of a graph. Experiments show that the new algorithms produce clearly better approximations than the original simple algorithm by Călinescu et al.