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A simulated annealing algorithm for the maximum planar subgraph problem

Timo Poranen
<span title="">2004</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/y4k3i2fvabgarkvywismzvy23a" style="color: black;">International Journal of Computer Mathematics</a> </i> &nbsp;
The maximum planar subgraph problem (MPS) is defined as follows: given a graph G, find a largest planar subgraph of G.  ...  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  ...  Acknowledgements The author thanks the anonymous referees for their valuable comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207160410001684352">doi:10.1080/00207160410001684352</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lyb2sijmnzfidjwajjcq7z2tf4">fatcat:lyb2sijmnzfidjwajjcq7z2tf4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830034019/http://www.sis.uta.fi/~tp54752/pub/new-mps.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/96/e0/96e0721d63aa9fcb6774942bd3ed3c8e8f2a0e70.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207160410001684352"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

A Note on the Practicality of Maximal Planar Subgraph Algorithms [article]

Markus Chimani, Karsten Klein, Tilo Wiedera
<span title="2016-08-26">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Given a graph G, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of G with the maximum number of edges.  ...  Surprisingly, a seemingly only theoretically strong approximation forms the building block of the strongest choice.  ...  They usually lack sophisticated algorithms for finding large planar subgraphs. first consider the pure problem of obtaining a planar subgraph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1608.07505v1">arXiv:1608.07505v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mgexneb2qndlpjbnwquzlvnxfy">fatcat:mgexneb2qndlpjbnwquzlvnxfy</a> </span>
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Computational Study on a PTAS for Planar Dominating Set Problem

Marjan Marzban, Qian-Ping Gu
<span title="2013-01-21">2013</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/63zsvf7vxzfznojpqgfvpyk2lu" style="color: black;">Algorithms</a> </i> &nbsp;
It is mentioned that the framework can be applied to obtain an O(2 ck n) time, c is a constant, (1 + 1/k)-approximation algorithm for the planar dominating set problem.  ...  Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs.  ...  Acknowledgements The authors thank the anonymous reviewers for their constructive comments. Algorithms 2013, 6  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/a6010043">doi:10.3390/a6010043</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u6dugxkniza25dqs56wejmwh6m">fatcat:u6dugxkniza25dqs56wejmwh6m</a> </span>
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Beyond trees: MRF inference via outer-planar decomposition

Dhruv Batra, A. C. Gallagher, Devi Parikh, Tsuhan Chen
<span title="">2010</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ilwxppn4d5hizekyd3ndvy2mii" style="color: black;">2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition</a> </i> &nbsp;
We leverage a new class of graphs amenable to exact inference, called outerplanar graphs, and propose an approximate inference algorithm called Outer-Planar Decomposition (OPD).  ...  Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NP-hard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate  ...  We thank Pedro Felzenszwalb for pointing out the connections between outer-planar graphs and k-trees, and Carlos Guestrin and Ramin Zabih for helpful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cvpr.2010.5539951">doi:10.1109/cvpr.2010.5539951</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cvpr/BatraGPC10.html">dblp:conf/cvpr/BatraGPC10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zpodxtnqabbm7c6w5ozwgfq7qe">fatcat:zpodxtnqabbm7c6w5ozwgfq7qe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150310223741/https://filebox.ece.vt.edu/~parikh/Publications/BatraGallagherParikhChen_CVPR2010_OPD.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ff/7c/ff7c76a2017ec01ea0746fc4943ee9d65d2a7c06.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cvpr.2010.5539951"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Approximation Algorithms for the Maximum Induced Planar and Outerplanar Subgraph Problems

Kerri Morgan, Graham Farr
<span title="">2007</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
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.  ...  Acknowledgments We thank the referees for their helpful comments. K. Morgan et al., Algorithms for MIPS , JGAA, 11 (1) 165-193 (2007)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00141">doi:10.7155/jgaa.00141</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/472ryjbh25amvkdipm5uourhum">fatcat:472ryjbh25amvkdipm5uourhum</a> </span>
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Heuristics for the Maximum Outerplanar Subgraph Problem

Timo Poranen
<span title="">2005</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/recosugx7nevfmgxg6453uyd3a" style="color: black;">Journal of Heuristics</a> </i> &nbsp;
We also use the solutions from the greedy heuristics as initial solutions for a simulated annealing algorithm.  ...  In this paper we compare solution quality and running times of different heuristics for finding maximum outerplanar subgraphs.  ...  Acknowledgments The author thanks the anonymous referees for their valuable comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10732-005-6999-6">doi:10.1007/s10732-005-6999-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/64d2gevefnb75htnbtoau3paly">fatcat:64d2gevefnb75htnbtoau3paly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809012616/https://grid.cs.gsu.edu/~cscazz/CS4520/project6520p.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/33/87/3387d9f44ee63dbce11ab3ff9472a39195c04f06.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10732-005-6999-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On maximum planar induced subgraphs

Luerbio Faria, Celina M. Herrera de Figueiredo, Sylvain Gravier, Candido F.X. de Mendonça, Jorge Stolfi
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Finally, we exhibit a polynomial-time 3 4 -approximation algorithm for finding a maximum planar induced subgraph of a maximum degree 3 graph.  ...  We prove that unless P = NP there is no polynomial-time approximation algorithm with fixed ratio to compute the size of a maximum planar induced subgraph for graphs in general.  ...  Acknowledgements We thank the referees for their careful reading and valuable suggestions which helped to improve the results and the presentation of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2006.03.021">doi:10.1016/j.dam.2006.03.021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ftyylh643rdnjedl7ys26332zq">fatcat:ftyylh643rdnjedl7ys26332zq</a> </span>
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An Algorithm for Finding Large Induced Planar Subgraphs [chapter]

Keith Edwards, Graham Farr
<span title="">2002</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This paper presents an efficient algorithm that finds an induced planar subgraph of at least 3n/(d + 1) vertices in a graph of n vertices and maximum degree d.  ...  Our algorithm builds up an induced planar subgraph by iteratively adding a new vertex to it, or swapping a vertex in it with one outside it, in such a way that the procedure is guaranteed to stop, and  ...  Halldórsson [11] gives an approximation algorithm that finds an induced planar subgraph of size Ω(n −1 (log n/ log log n) 2 ) times the optimum.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45848-4_6">doi:10.1007/3-540-45848-4_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/npgkvhcnffbvlhnao3wdnoulue">fatcat:npgkvhcnffbvlhnao3wdnoulue</a> </span>
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On approximating the d -girth of a graph

David Peleg, Ignasi Sau, Mordechai Shalom
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
For a finite, simple, undirected graph G and an integer d ≥ 1, a mindeg-d subgraph is a subgraph of G of minimum degree at least d.  ...  The current article further explores the complexity of finding a small mindeg-d subgraph of a given graph (that is, approximating its d-girth), by providing new hardness results and the first approximation  ...  to the problem of finding a d-regular subgraph of minimum size.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2013.04.022">doi:10.1016/j.dam.2013.04.022</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5zzhqyjmzjglpeufl2t2fixxtu">fatcat:5zzhqyjmzjglpeufl2t2fixxtu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829182737/http://www.lirmm.fr/~sau/Pubs/d-girthFULL.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2e/bb/2ebb12d3c49dfcfb5a1d5aaf25019d94e72b985f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2013.04.022"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

On Approximating the d-Girth of a Graph [chapter]

David Peleg, Ignasi Sau, Mordechai Shalom
<span title="">2011</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
For a finite, simple, undirected graph G and an integer d ≥ 1, a mindeg-d subgraph is a subgraph of G of minimum degree at least d.  ...  The current article further explores the complexity of finding a small mindeg-d subgraph of a given graph (that is, approximating its d-girth), by providing new hardness results and the first approximation  ...  For any fixed d ≥ 3, finding a constant-factor polynomial-time approximation algorithm for the d-girth problem in the class of graphs k≥0 G 2 k d is NP- hard.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-18381-2_39">doi:10.1007/978-3-642-18381-2_39</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/24lhgvf2ijakbmzxegjzg7utcy">fatcat:24lhgvf2ijakbmzxegjzg7utcy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809115023/http://www.lirmm.fr/~sau/Pubs/PSS11.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/29/cb/29cb80edcbf183706bd13c496dc5eb12eb8a9f5d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-18381-2_39"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Approximating the minimum hub cover problem on planar graphs

Belma Yelbay, Ş. İlker Birbil, Kerem Bülbül, Hasan Jamil
<span title="2015-03-31">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5dkx5l3pkjclfd46nyh4eftsrq" style="color: black;">Optimization Letters</a> </i> &nbsp;
We study an approximation algorithm with a performance guarantee to solve a new NP-hard optimization problem on planar graphs.  ...  Our algorithm is based on a well-known graph decomposition technique that partitions the graph into a set of outerplanar graphs and provides an approximate solution with a proven performance ratio.  ...  Proposition 3.1 gives a formal proof of this statement. Proposition 3.1. Algorithm 1 finds an approximate hub cover for a planar graph which is at most (k + 1)/k optimal. Proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11590-015-0876-5">doi:10.1007/s11590-015-0876-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xzmopsaflrgjtdsl7nnridg2my">fatcat:xzmopsaflrgjtdsl7nnridg2my</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809033230/https://research.sabanciuniv.edu/27188/1/MHC_Planar_Application.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a7/19/a71941d878343b57c9e3b61a0b96190d5e97f56a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11590-015-0876-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Approximation Schemes for Minimum 2-Connected Spanning Subgraphs in Weighted Planar Graphs [chapter]

André Berger, Artur Czumaj, Michelangelo Grigni, Hairong Zhao
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Prior to our work, for all these problems no polynomial or quasi-polynomial time algorithms were known to achieve an approximation ratio better than 2.  ...  From this we derive quasi-polynomial time approximation schemes for the problems of finding the minimum-weight 2-edge-connected or biconnected spanning subgraph in planar graphs.  ...  Let ε > 0, and let G be a weighted planar graph with n vertices. There is an algorithm running in time n O(log n·log(1/ε)/ε) that outputs a {1,2}-VCSS H of G such that w(H) ≤ (1 + ε) · OPT.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11561071_43">doi:10.1007/11561071_43</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m565l4ypivaafiuyt6vvzq5goe">fatcat:m565l4ypivaafiuyt6vvzq5goe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060901192135/http://ems.calumet.purdue.edu/mcss/zhao/papers/esa05.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fd/65/fd655589012b90793dad2841a6936abe75374758.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11561071_43"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Planarization and Acyclic Colorings of Subcubic Claw-Free Graphs [chapter]

Christine Cheng, Eric McDermid, Ichiro Suzuki
<span title="">2011</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
From an approximability point of view, we show that our results imply 6/5-and 9/8-approximation algorithms, respectively, for the (NP-hard) problems of finding a maximum induced planar subgraph and a maximum  ...  planar subgraph of a subcubic claw-free graph, respectively.  ...  We now show that the planar subgraph found by the edge deletions described in the above procedure is a 9/8-approximation algorithm for MAXPS.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-25870-1_11">doi:10.1007/978-3-642-25870-1_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ylmxr6wzg5bzpnp5bvx3vbmudm">fatcat:ylmxr6wzg5bzpnp5bvx3vbmudm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808094436/http://www.cs.uwm.edu/faculty/ccheng/papers/WGMcDermidSubmission-long.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/05/19/051930a3a476b48978f35540cc276f24bd252442.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-25870-1_11"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Planarizing Graphs - A Survey and Annotated Bibliography

Annegret Liebers
<span title="">2001</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph.  ...  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.  ...  Approximations and Heuristics First consider a trivial approximation for finding a maximum planar subgraph by observing that for a given graph G with n vertices, any spanning tree of G is a planar subgraph  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00032">doi:10.7155/jgaa.00032</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zftlx3a5jnesxff5hjymjewp5u">fatcat:zftlx3a5jnesxff5hjymjewp5u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814094359/http://www.univie.ac.at/EMIS/journals/JGAA/accepted/01/Liebers01.5.1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/12/8c/128cae66d00ecb3e429e55b645463e63eb3ba987.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00032"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Advances in the Planarization Method: Effective Multiple Edge Insertions

Markus Chimani, Carsten Gutwenger
<span title="">2012</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
The planarization method is the strongest known method to heuristically find good solutions to the general crossing number problem in graphs: Starting from a planar subgraph, one iteratively inserts edges  ...  Thereby, we also present the first implementation of an approximation algorithm for the crossing number problem of general graphs.  ...  For each graph instance, all edge insertion algorithms were called with the same, pre-computed maximal planar subgraph, which was computed using OGDF's PQ-tree based planar subgraph algorithm [22] (best  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00264">doi:10.7155/jgaa.00264</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c6z5aesvkbdxhhmg6ketj7ukia">fatcat:c6z5aesvkbdxhhmg6ketj7ukia</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921222847/http://emis.maths.tcd.ie/EMIS/journals/JGAA/accepted/2012/ChimaniGutwenger2012.16.3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/76/68/76681ecc8f3b99a2e84782610ca95fcb7ff359a8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00264"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>
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