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

Kazuhiro Kurita, Kunihiro Wasa, Alessio Conte, Takeaki Uno, Hiroki Arimura
2018 Lecture Notes in Computer Science  
We propose two algorithms, for 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.  ... 
doi:10.1007/978-3-319-94667-2_17 fatcat:rc6knbovwrb6zb3kejc4g5pyqe

On the complexity of various parameterizations of common induced subgraph isomorphism

Faisal N. Abu-Khzam, Édouard Bonnet, Florian Sikora
2017 Theoretical Computer Science  
Both problems are shown to be W[1]-complete on bipartite graphs 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.  ... 
doi:10.1016/j.tcs.2017.07.010 fatcat:dabbehi67bcwlmjt2ygu67b5dy

An efficient exhaustive low-weight codeword search for structured LDPC codes

S. M. Khatami, L. Danjean, D. V. Nguyen, B. Vasic
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 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.  ... 
doi:10.1109/ita.2013.6502981 dblp:conf/ita/KhatamiDNV13 fatcat:g57btjlfmfh7rgp7voyg5x7b6a

On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism [chapter]

Faisal N. Abu-Khzam, Édouard Bonnet, Florian Sikora
2015 Lecture Notes in Computer Science  
In the Maximum Common 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.  ... 
doi:10.1007/978-3-319-19315-1_1 fatcat:knzdi3nve5ao7kvxr7ubulpdnq

On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism [article]

Faisal N. Abu-Khzam, Édouard Bonnet, Florian Sikora
2017 arXiv   pre-print
In the Maximum Common 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.  ... 
arXiv:1412.1261v2 fatcat:ownbquhznvcrnmz4uthnys5o3m

An Modified Cole's Importance Sampling Method For Low Error Floor QC-LDPC Codes Construction [article]

Vasiliy Usatyuk
2022 arXiv   pre-print
We modified Cole's Importance Sampling (IS) method for 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.  ... 
arXiv:2208.05795v1 fatcat:eec24wsnwbamhhkvczhscrxncq

Induced subgraphs of induced subgraphs of large chromatic number [article]

António Girão, Freddie Illingworth, Emil Powierski, Michael Savery, Alex Scott, Youri Tamitegama, Jane Tan
2022 arXiv   pre-print
We prove that, for every graph F 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  ... 
arXiv:2203.03612v2 fatcat:n4a7wstixzhwnjrmprtowhsuam

On the Construction of Structured LDPC Codes Free of Small Trapping Sets

Dung Viet Nguyen, Shashi Kiran Chilappagari, Michael W. Marcellin, Bane Vasic
2012 IEEE Transactions on Information Theory  
This description uses Latin squares to define a set 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  ... 
doi:10.1109/tit.2011.2173733 fatcat:ayxryp2bvnh3zj5j4cn3m7kque

Subgraph Isomorphism in Planar Graphs and Related Problems [article]

David Eppstein
1999 arXiv   pre-print
The same methods can be used to solve other planar graph problems including connectivity, diameter, 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.  ... 
arXiv:cs/9911003v1 fatcat:dodamhrjcfcp7dczhpsziwvztm

Subgraph Isomorphism in Planar Graphs and Related Problems

David Eppstein
1999 Journal of Graph Algorithms and Applications  
The same methods can be used to solve other planar graph problems including connectivity, diameter, 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.  ... 
doi:10.7155/jgaa.00014 fatcat:wachtewscvh2ngaz5pygzjrddy

Subgraph Isomorphism in Planar Graphs and Related Problems [chapter]

David Eppstein
2002 Graph Algorithms and Applications I  
The same methods can be used to solve other planar graph problems including connectivity, diameter, 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.  ... 
doi:10.1142/9789812777638_0014 fatcat:odmviuipk5e4ncqlbxhwsofete

Decomposing a Graph Into Expanding Subgraphs [chapter]

Guy Moshkovitz, Asaf Shapira
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
recently shown that every graph 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).  ... 
doi:10.1137/1.9781611973730.85 dblp:conf/soda/MoshkovitzS15 fatcat:ojdugwnaavd4biqm3ug4ahmski

Decomposing a Graph Into Expanding Subgraphs [article]

Guy Moshkovitz, Asaf Shapira
2015 arXiv   pre-print
These 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 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).  ... 
arXiv:1502.00409v1 fatcat:4zhtc665sba3rfvcyu2ouzrtfm

Fast Distributed Algorithms for Girth, Cycles and Small Subgraphs

Keren Censor-Hillel, Orr Fischer, Tzlil Gonen, François Le Gall, Dean Leitersdorf, Rotem Oshman, Hagit Attiya
2020 International Symposium on Distributed Computing  
Next, we introduce a new technique (the partition tree technique) allowing for 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.  ... 
doi:10.4230/lipics.disc.2020.33 dblp:conf/wdag/Censor-HillelFG20 fatcat:hwcxvuyy5zbp3arzoxmmnt7d3i

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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