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Efficient Enumeration of Subgraphs and Induced Subgraphs with Bounded Girth
[chapter]

2018
*
Lecture Notes in Computer Science
*

We propose two algorithms, for

doi:10.1007/978-3-319-94667-2_17
fatcat:rc6knbovwrb6zb3kejc4g5pyqe
*enumerating*respectively vertex*induced**subgraphs**and*edge*induced**subgraphs**with**bounded**girth*, both running in O(n) amortized time per solution*and*using O(n^3) space. ... In this paper, we consider the problem*of*listing connected*subgraphs**with**bounded**girth*. As a large*girth*is index*of*sparsity, this allows to extract sparse structures from the input graph. ... Problem 1 k-*girth*connected*induced**subgraph**enumeration*.*Enumerate*all connected*induced**subgraphs*S*of*a graph G*with*g(S) ≥ k, without duplicates. Problem 2 k-*girth*connected*subgraph**enumeration*. ...##
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On the complexity of various parameterizations of common induced subgraph isomorphism

2017
*
Theoretical Computer Science
*

Both problems are shown to be W[1]-complete on bipartite graphs

doi:10.1016/j.tcs.2017.07.010
fatcat:dabbehi67bcwlmjt2ygu67b5dy
*and*graphs*of**girth*five*and*, unless P = NP, they do not to belong to the class XP when parameterized by a*bound*on the size*of*the minimum ... Maximum Common*Induced**Subgraph*(henceforth MCIS) is among the most studied classical NP-hard problems. ... Concerning its classical complexity, Maximum Common*Induced**Subgraph*is NP-complete,*and*remains so on bipartite graphs*and*graphs*with**bounded*treewidth. ...##
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An efficient exhaustive low-weight codeword search for structured LDPC codes

2013
*
2013 Information Theory and Applications Workshop (ITA)
*

In this paper, we present an algorithm to find all low-weight codewords in a given quasi-cyclic (QC) low-density parity-check (LDPC) code

doi:10.1109/ita.2013.6502981
dblp:conf/ita/KhatamiDNV13
fatcat:g57btjlfmfh7rgp7voyg5x7b6a
*with*a fixed column-weight*and**girth*. ... The proposed search method relies on the knowledge*of*possible topologies*of*such smaller trapping sets present in a code ensemble, which enables an*efficient*search. ... Lemma 1*and*2 are presented in order to*bound*the categories*of*weight-14 codewords in C n (3, d c , 8) . Proof: Assume there exists a weight-14 codeword*with**girth*8*with*a check node*of*degree-6. ...##
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On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism
[chapter]

2015
*
Lecture Notes in Computer Science
*

In the Maximum Common

doi:10.1007/978-3-319-19315-1_1
fatcat:knzdi3nve5ao7kvxr7ubulpdnq
*Induced**Subgraph*problem (henceforth MCIS), given two graphs G 1*and*G 2 , one looks for a graph*with*the maximum number*of*vertices being both an*induced**subgraph**of*G 1*and*G 2 ... This kind*of*tight lower*bound*has been shown for a few problems*and*parameters but, to the best*of*our knowledge, not for the vertex cover number. ... Corollary 6 . 6 Maximum Common*Induced**Subgraph**and*Maximum Common Connected*Induced**Subgraph*remain W[1]-complete on bipartite graphs*of**girth*6*and*degeneracy 2. ...##
###
On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism
[article]

2017
*
arXiv
*
pre-print

In the Maximum Common

arXiv:1412.1261v2
fatcat:ownbquhznvcrnmz4uthnys5o3m
*Induced**Subgraph*problem (henceforth MCIS), given two graphs G_1*and*G_2, one looks for a graph*with*the maximum number*of*vertices being both an*induced**subgraph**of*G_1*and*G_2. ... This kind*of*tight lower*bound*has been shown for a few problems*and*parameters but, to the best*of*our knowledge, not for the vertex cover number. ... Corollary 6 . 6 Maximum Common*Induced**Subgraph**and*Maximum Common Connected*Induced**Subgraph*remain W[1]-complete on bipartite graphs*of**girth*6*and*degeneracy 2. ...##
###
An Modified Cole's Importance Sampling Method For Low Error Floor QC-LDPC Codes Construction
[article]

2022
*
arXiv
*
pre-print

We modified Cole's Importance Sampling (IS) method for

arXiv:2208.05795v1
fatcat:eec24wsnwbamhhkvczhscrxncq
*enumerating**of*Trapping Sets (TS, asymmetric*subgraphs*) causing an error under message-passing decoder. ... Its allowed superior Velasquez-Subramani*and*Karimi-Banihashemi TS*enumerating*methods. ... It was one the most well described*with*application for well know codes*and**efficient*method for TS*enumerating*. ...##
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Induced subgraphs of induced subgraphs of large chromatic number
[article]

2022
*
arXiv
*
pre-print

We prove that, for every graph F

arXiv:2203.03612v2
fatcat:n4a7wstixzhwnjrmprtowhsuam
*with*at least one edge, there is a constant c_F such that there are graphs*of*arbitrarily large chromatic number*and*the same clique number as F in which every F-free*induced*... This generalises recent theorems*of*Briański, Davies*and*Walczak,*and*Carbonero, Hompe, Moore*and*Spirkl. Moreover, we show an analogous statement where clique number is replaced by odd*girth*. ... For every graph F*with*at least one cycle, there exists a constant b F*and*graphs G*of*arbitrarily large chromatic number*and*the same*girth*as F such that every F -free*induced**subgraph**of*G is b F -colourable ...##
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On the Construction of Structured LDPC Codes Free of Small Trapping Sets

2012
*
IEEE Transactions on Information Theory
*

This description uses Latin squares to define a set

doi:10.1109/tit.2011.2173733
fatcat:ayxryp2bvnh3zj5j4cn3m7kque
*of*permutation matrices that have disjoint support*and*to derive a simple necessary*and*sufficient condition for the Tanner graph*of*a code to be free ... We present a method to construct low-density paritycheck (LDPC) codes*with*low error floors on the binary symmetric channel. ... Chilappagari was performed when he was*with*the Department*of*Electrical*and*Computer Engineering, University*of*Arizona, Tucson. Professor Marcellin is a Fellow*of*the IEEE,*and*is a member*of*Tau ...##
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Subgraph Isomorphism in Planar Graphs and Related Problems
[article]

1999
*
arXiv
*
pre-print

The same methods can be used to solve other planar graph problems including connectivity, diameter,

arXiv:cs/9911003v1
fatcat:dodamhrjcfcp7dczhpsziwvztm
*girth*,*induced**subgraph*isomorphism,*and*shortest paths. ... We solve the*subgraph*isomorphism problem in planar graphs in linear time, for any pattern*of*constant size. ... 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

1999
*
Journal of Graph Algorithms and Applications
*

The same methods can be used to solve other planar graph problems including connectivity, diameter,

doi:10.7155/jgaa.00014
fatcat:wachtewscvh2ngaz5pygzjrddy
*girth*,*induced**subgraph*isomorphism,*and*shortest paths. ... Several papers have studied planar*subgraph*isomorphism*with*restricted patterns. ... 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
*

The same methods can be used to solve other planar graph problems including connectivity, diameter,

doi:10.1142/9789812777638_0014
fatcat:odmviuipk5e4ncqlbxhwsofete
*girth*,*induced**subgraph*isomorphism,*and*shortest paths. ... Several papers have studied planar*subgraph*isomorphism*with*restricted patterns. ... Acknowledgements The author wishes to thank Sandy Irani, George Lueker,*and*the anonymous referees, for helpful comments on drafts*of*this paper. ...##
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Decomposing a Graph Into Expanding Subgraphs
[chapter]

2014
*
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
*

recently shown that every graph

doi:10.1137/1.9781611973730.85
dblp:conf/soda/MoshkovitzS15
fatcat:ojdugwnaavd4biqm3ug4ahmski
*with*average degree d contains an n-vertex*subgraph**with*average degree at least (1 − o(1))d*and*vertex expansion 1/ log 1+o(1) n. ... The above results are obtained as corollaries*of*a new family*of*graphs, which we construct by picking random*subgraphs**of*the hypercube,*and*analyze using (simple) arguments from the theory*of*metric ... Lemma 3. 3 . 3 Any (not necessarily*induced*)*subgraph**of*the d-cube*with*t vertices*and*average degree r has edge expansion at most 2r log d/ log(t/2). ...##
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Decomposing a Graph Into Expanding Subgraphs
[article]

2015
*
arXiv
*
pre-print

These results are obtained as corollaries

arXiv:1502.00409v1
fatcat:4zhtc665sba3rfvcyu2ouzrtfm
*of*a new family*of*graphs, which we construct by picking random*subgraphs**of*the hypercube,*and*analyze using (simple) arguments from the theory*of*metric embedding ... Our goal in this paper is to show that in several*of*the instantiations*of*the above approach, the quantitative*bounds*that were obtained are essentially best possible. ... Lemma 3. 3 . 3 Any (not necessarily*induced*)*subgraph**of*the d-cube*with*t vertices*and*average degree r has edge expansion at most 2r log d/ log(t/2). ...##
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Fast Distributed Algorithms for Girth, Cycles and Small Subgraphs

2020
*
International Symposium on Distributed Computing
*

Next, we introduce a new technique (the partition tree technique) allowing for

doi:10.4230/lipics.disc.2020.33
dblp:conf/wdag/Censor-HillelFG20
fatcat:hwcxvuyy5zbp3arzoxmmnt7d3i
*efficiently*listing all copies*of*any*subgraph*, which is deterministic*and*improves upon the state-*of*the-art for non-dense ... In this paper we give fast distributed graph algorithms for detecting*and*listing small*subgraphs*,*and*for computing or approximating the*girth*. ... This*induces*a rich landscape*of*complexities for*subgraph*-related problems. ...##
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Page 775 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

The author also uses this technique to construct

*efficient*algo- rithms for a number*of*other decision*and**enumeration*problems for planar graphs, including connectivity, diameter,*girth*,*induced**subgraph*... Summary: “After introducing the definitions*of*decomposition, Ramsey decomposition*and*critical Ramsey decomposition, we deduce some propositions*of*these kinds*of*decompositions*and*a lower*bound*formula ...
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