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A Linear-Time Algorithm for Finding Induced Planar Subgraphs

2018
*
Symposium on Experimental and Efficient Algorithms
*

In contrast, we propose

doi:10.4230/lipics.sea.2018.23
dblp:conf/wea/HuangBCZZ18
fatcat:ef4jnwwyqne2nidxf2n7rtvd7i
*a**linear*-*time**algorithm*that*finds*an*induced**planar**subgraph*of n − ν vertices in*a*graph of n vertices, where ν denotes the total number of vertices shared by the detected Kuratowski ... Edwards and Farr proposed an*algorithm*with O(mn)*time*complexity to*find*an*induced**planar**subgraph*of at least 3n/(d + 1) vertices in*a*graph of maximum degree d. ... x 6234567917*Linear*-*Time**Algorithm**for**Finding**Induced**Planar*SubgraphsAlgorithm 2: WalkdownWithSkips( Ḡ, v c ). ...##
###
Approximation Algorithms for the Maximum Induced Planar and Outerplanar Subgraph Problems

2007
*
Journal of Graph Algorithms and Applications
*

The task of

doi:10.7155/jgaa.00141
fatcat:472ryjbh25amvkdipm5uourhum
*finding*the largest subset of vertices of*a*graph that*induces**a**planar**subgraph*is known as the Maximum*Induced**Planar**Subgraph*problem (MIPS). ... Efficient*algorithms**for**finding*large*induced*outerplanar graphs are also given. ... Acknowledgments We thank the referees*for*their helpful comments. K. Morgan et al.,*Algorithms**for*MIPS , JGAA, 11 (1) 165-193 (2007) ...##
###
An Algorithm for Finding Large Induced Planar Subgraphs
[chapter]

2002
*
Lecture Notes in Computer Science
*

This paper presents an efficient

doi:10.1007/3-540-45848-4_6
fatcat:npgkvhcnffbvlhnao3wdnoulue
*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 ... In this paper, we present*a*polynomial*time**algorithm*that*finds*an*induced**planar**subgraph*of at least 3n/(d + 1) vertices in*a*graph of maximum degree d. ...##
###
Planarizing Graphs - A Survey and Annotated Bibliography

2001
*
Journal of Graph Algorithms and Applications
*

Given

doi:10.7155/jgaa.00032
fatcat:zftlx3a5jnesxff5hjymjewp5u
*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. ... [DT89] obtains an O(m log n)*time**algorithm**for**finding**a*maximal*planar**subgraph*as*a*byproduct of an*algorithm**for*incremental*planarity*testing. ...##
###
Planar Induced Subgraphs of Sparse Graphs

2015
*
Journal of Graph Algorithms and Applications
*

These results are constructive, implying

doi:10.7155/jgaa.00358
fatcat:whom2r4wfzhu3cthim45nkt3ca
*linear*-*time**algorithms*to*find*the respective*induced**subgraphs*. ... We show that every graph has an*induced*pseudoforest of at least n-m/4.5 vertices, an*induced*partial 2-tree of at least n-m/5 vertices, and an*induced**planar**subgraph*of at least n-m/5.2174 vertices. ... The*planarization*problem Goal:*find*big*planar**subgraphs*in nonplanar graphs Equivalently: delete as little as possible so the rest is*planar*In the version we study, the*planar**subgraphs*are*induced*...##
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Subgraph Isomorphism in Planar Graphs and Related Problems

1999
*
Journal of Graph Algorithms and Applications
*

We solve the

doi:10.7155/jgaa.00014
fatcat:wachtewscvh2ngaz5pygzjrddy
*subgraph*isomorphism problem in*planar*graphs in*linear**time*,*for*any pattern of constant size. ... Plehn and Voigt [41] give an*algorithm**for**subgraph*isomorphism which in*planar*graphs takes*time*), but this is still much larger than the*linear*bound we achieve. ... Acknowledgements The author wishes to thank Sandy Irani, George Lueker, and the anonymous referees,*for*helpful comments on drafts of this paper. ...##
###
Subgraph Isomorphism in Planar Graphs and Related Problems
[chapter]

2002
*
Graph Algorithms and Applications I
*

We solve the

doi:10.1142/9789812777638_0014
fatcat:odmviuipk5e4ncqlbxhwsofete
*subgraph*isomorphism problem in*planar*graphs in*linear**time*,*for*any pattern of constant size. ... Plehn and Voigt [41] give an*algorithm**for**subgraph*isomorphism which in*planar*graphs takes*time*), but this is still much larger than the*linear*bound we achieve. ... Acknowledgements The author wishes to thank Sandy Irani, George Lueker, and the anonymous referees,*for*helpful comments on drafts of this paper. ...##
###
Subgraph Isomorphism in Planar Graphs and Related Problems
[article]

1999
*
arXiv
*
pre-print

We solve the

arXiv:cs/9911003v1
fatcat:dodamhrjcfcp7dczhpsziwvztm
*subgraph*isomorphism problem in*planar*graphs in*linear**time*,*for*any pattern of constant size. ... The same methods can be used to solve other*planar*graph problems including connectivity, diameter, girth,*induced**subgraph*isomorphism, and shortest paths. ... Acknowledgements The author wishes to thank Sandy Irani, George Lueker, and the anonymous referees,*for*helpful comments on drafts of this paper. ...##
###
Planar Induced Subgraphs of Sparse Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

These results are constructive, implying

doi:10.1007/978-3-662-45803-7_1
fatcat:4e4z2ybn4zavjptajkyjvinyri
*linear*-*time**algorithms*to*find*the respective*induced**subgraphs*. ... We show that every graph has an*induced*pseudoforest of at least n − m/4.5 vertices, an*induced*partial 2-tree of at least n − m/5 vertices, and an*induced**planar**subgraph*of at least n − m/5.2174 vertices ... The authors thank Amir Nayyeri*for*helpful discussions. ...##
###
Arboricity and bipartite subgraph listing algorithms

1994
*
Information Processing Letters
*

In graphs of bounded arboricity, the total complexity of all maximal complete bipartite

doi:10.1016/0020-0190(94)90121-x
fatcat:ej4wcu747ne2rhvlgbcj2fnbda
*subgraphs*is O(n). We describe*a**linear**time**algorithm*to list such*subgraphs*. ... The arboricity bound is necessary:*for*any constant k and any n there exists an n-vertex graph with O(n) edges and (n/ log n) k maximal complete bipartite*subgraphs*K k, . ...*A*decomposition of*a**planar*graph into three forests can be found in*linear**time*[7, 18] . ...##
###
Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs

2019
*
International Symposium on Parameterized and Exact Computation
*

Consider the following problem: given

doi:10.4230/lipics.ipec.2019.23
dblp:conf/iwpec/NovotnaOPRLW19
fatcat:lcgp6expunh4rlp3jjysmw6lsa
*a*graph G ∈ D,*find**a*largest, in terms of the number of vertices,*induced**subgraph*of G that belongs to C. ... This leads,*for*example, to the following corollaries*for*specific classes C and D:*a*largest*induced*forest in*a*Pt-free graph can be found in 2Õ (n 2/3 )*time*,*for*every fixed t; and*a*largest*induced*...*Algorithms**for*Max*Induced**Planar**Subgraph*and, more generally, Max*Induced*Σ-Embeddable*Subgraph*, were provided by Kociumaka and Pilipczuk [16] . ...##
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Parallel Planar Subgraph Isomorphism and Vertex Connectivity
[article]

2020
*
arXiv
*
pre-print

By using

arXiv:2007.01199v1
fatcat:tpkc6mmd5jbslcx6ftjzukfjia
*a*connection to certain separating cycles, our*subgraph*isomorphism*algorithm*can decide the vertex connectivity of*a**planar*graph (with high probability) in asymptotically near-*linear*work and ... Our randomized low depth*algorithm*has*a*near-*linear*work dependency on the size of the target graph. ... Eppstein presents the first FPT*subgraph*isomorphism*algorithm**for**planar*graphs that has*a**linear*dependency on the size of the pattern graph [19] . ...##
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An Alternative Method to Crossing Minimization on Hierarchical Graphs

2001
*
SIAM Journal on Optimization
*

Based on

doi:10.1137/s1052623498334013
fatcat:7qbe5ufra5a3jcepeqgdgggelm
*a*characterization of 2-level*planar*graphs, we give an integer*linear*programming formulation*for*the 2-level*planarization*problem. ... First, we give*a*motivation*for*our approach. Then, we address the problem of extracting*a*2-level*planar**subgraph*of maximum weight in*a*given 2-level graph. This problem is NP-hard. ... We build our hope on the fact that there is*a**linear**time**algorithm**for*recognizing h-level*planar*graphs (see [HP96] and [BN88] ). ...##
###
On drawing a graph convexly in the plane (extended abstract)
[chapter]

1995
*
Lecture Notes in Computer Science
*

We obtain

doi:10.1007/3-540-58950-3_358
fatcat:6mem7zatwvcotmuexbu6rjfdum
*a*necessary and sufficient condition*for*the existence and*a**linear*Mgorithm*for*the construction of such an extension. ... Let G be*a**planar*graph and H be*a**subgraph*of G. Given any convex drawing of H, we investigate the problem of how to extend the drawing of H to*a*convex drawing of G. ... [5] construct*a**linear**algorithm*that*finds*an extendible outer faciM cycle of G by applying the*algorithms**for**finding*the triconnected components of G [8] and*for**planarity*testing [9] on*a*graph ...##
###
Page 7016 of Mathematical Reviews Vol. , Issue 89M
[page]

1989
*
Mathematical Reviews
*

*A*

*linear*decision tree queries COMPUTER SCIENCE 7016 “f(x) > 0”

*for*

*a*

*linear*function f. ... Analogously,

*a*graph G is said to be an

*induced*minor of H if G is obtained from an

*induced*

*subgraph*of H by edge contraction. ...

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