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Efficient Enumeration of Induced Subtrees in a K-Degenerate Graph
[chapter]

2014
*
Lecture Notes in Computer Science
*

In this paper, we address the problem of

doi:10.1007/978-3-319-13075-0_8
fatcat:5elaatgm2zbddlvmvrkmnxreyu
*enumerating*all*induced*subtrees in*an*input k-degenerate graph, where*an**induced*subtree is*an*acyclic and connected*induced**subgraph*. ...*Induced*subtrees are fundamental object thus it should be studied deeply and there possibly exist some*efficient**algorithms*. ... Acknowledgement This work was partially supported by MEXT Grant-in-Aid*for*Scientific Research (A) 24240021 and Grant-in-Aid*for*JSPS Fellows 25 · 1149. ...##
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Efficient Exact Algorithms for Maximum Balanced Biclique Search in Bipartite Graphs
[article]

2020
*
arXiv
*
pre-print

To further speed up this

arXiv:2007.08836v1
fatcat:dkfq624d6vfb5lzgpqcy5yxgc4
*algorithm*, tighter upper*bounds*, faster heuristics and effective reductions are proposed, allowing*an*MBB to be discovered within a few seconds*for*bipartite graphs*with*millions ...*algorithm**for*dense bipartite graphs on each of the*subgraphs*. ... and bicore based optimizations bd3 hbvMBB without branching technique bd4 hbvMBB*with*degree order bd5 hbvMBB*with**degeneracy*order degOrder*Algorithm**for**degeneracy*order Table 4 : 4*Efficiency*...##
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FPT Algorithms for Finding Near-Cliques in c-Closed Graphs
[article]

2021
*
arXiv
*
pre-print

We study various established notions of such substructures, including k-plexes, complements of

arXiv:2007.09768v4
fatcat:z6eu4ca7orez5cdiexwavuzgg4
*bounded*-*degeneracy*and*bounded*-treewidth graphs. ... In practice, due to noise in data, one wishes to actually discover "near-cliques", which can be characterized as cliques*with*a sparse*subgraph*removed. ... C*Bounded*co-*degeneracy*In this section, we give FPT*algorithms**for**enumerating*maximal*subgraph**with**bounded*co-*degeneracy*in a c-closed graph. ...##
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An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs
[article]

2019
*
arXiv
*
pre-print

In this paper, we propose a characterization of chordal bipartite graphs and

arXiv:1903.02161v1
fatcat:dsgsp66xuneaxfzaotnsp3e44e
*an**efficient**enumeration**algorithm**for*chordal bipartite*induced**subgraphs*. ... Moreover, we propose*an**algorithm*ECB which*enumerates*all chordal bipartite*induced**subgraphs*in O(ktΔ^2) time per solution on average, where k is the*degeneracy*, t is the maximum size of K_t,t as*an*... Let v be a maximum vertex in X*with*respect to inclusion of neighbors. If d(v) ≤ t, then the statement holds from Lemma 17. We assume that d(v) > t. ...##
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Efficient Enumeration of Bipartite Subgraphs in Graphs
[chapter]

2018
*
Lecture Notes in Computer Science
*

As the main results, we develop two

doi:10.1007/978-3-319-94776-1_38
fatcat:xr6pgqjd3bhmdcy2adnq3nqkgu
*efficient**algorithms*: the one*enumerates*all bipartite*induced**subgraphs*of a graph*with**degeneracy*k in O(k) time per solution. ... We propose the first non-trivial*algorithms**for**enumerating*all bipartite*subgraphs*in a given graph. ... In this paper, we propose*efficient**enumeration**algorithms**for*bipartite*induced**subgraphs*and bipartite*subgraphs*. ...##
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Finding Dense Subgraphs of Sparse Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

Furthermore, we obtain a fixedparameter

doi:10.1007/978-3-642-33293-7_23
fatcat:utinw4vbsfd3nhuxkikvbvxqhi
*algorithm**for*DkS*with*respect to the combined parameter "*degeneracy*of G and |V | − k". ... We investigate the computational complexity of the Densestk-*Subgraph*(DkS) problem, where the input is*an*undirected graph G = (V, E) and one wants to find a*subgraph*on exactly k vertices*with*a maximum ... We also give*an*observation about the*enumeration*of certain*subgraphs*in degree*bounded*graphs, which yields a subroutine used in our*algorithms*. Preparations. ...##
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Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six

2020
*
Innovations in Theoretical Computer Science
*

Our main theorem asserts linear time

doi:10.4230/lipics.itcs.2020.38
dblp:conf/innovations/BeraPS20
fatcat:crkyagghbzbcfh3gvd7qoy4esq
*algorithms**for*counting (up to) 5-vertex*subgraphs*in*bounded**degeneracy*graphs. ...*For*what values k, does the sub-cnt k problem admit a linear time*algorithm*in*bounded**degeneracy*graphs? ... But the*degeneracy*of G is just 2! (In any*induced**subgraph*of G , the minimum degree is at most 2, proving the*bound*.) ...##
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Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six
[article]

2019
*
arXiv
*
pre-print

In a classic result, Chiba and Nishizeki (SICOMP 85) gave linear time

arXiv:1911.05896v2
fatcat:ftxidoc4m5arhe53r44pu546qi
*algorithms**for*clique and 4-cycle counting*for**bounded**degeneracy*graphs. ... We consider the problem of counting all k-vertex*subgraphs*in*an*input graph,*for*any constant k. This problem (denoted sub-cnt_k) has been studied extensively in both theory and practice. ... In particular, David pointed out that the lower*bound**for*counting 8-cycles does not follow from our construction, as we erroneously claimed in the earlier version of this paper. ...##
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Scaling Up Maximal k-plex Enumeration
[article]

2022
*
arXiv
*
pre-print

Then, we develop a new branch-and-

arXiv:2203.10760v3
fatcat:7zpmmysp2za33ezzn6c7xijt4i
*bound**algorithm**with*a carefully-designed pivot re-selection strategy to*enumerate*all k-plexes, which outputs all k-plexes in O(n^2γ_k^n) time theoretically, where n ...*For*example, on a large real-world graph*with*more than 200 million edges, our parallel*algorithm*can finish the computation within two minutes, while the state-of-the-art parallel*algorithm*cannot terminate ... Let ( ) = ( , ( )) be*an**induced**subgraph*of if ⊆ and ( ) = {( , )|( , ) ∈ , ∈ , ∈ }. ...##
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Proximity Search For Maximal Subgraph Enumeration
[article]

2021
*
arXiv
*
pre-print

Bipartite

arXiv:1912.13446v3
fatcat:aiwlhrezcjbyrelpcxe45jb7zu
*Subgraphs*, Maximal k-Degenerate*Subgraphs*(*for**bounded*k), Maximal*Induced*Chordal*Subgraphs*, and Maximal*Induced*Trees. ... This paper proposes a new general technique*for*maximal*subgraph**enumeration*which we call proximity search, whose aim is to design*efficient**enumeration**algorithms**for*problems that could not be solved ... ACKNOWLEDGEMENTS We wish to thank the anonymous reviewers*for*their thorough analysis of the paper, which helped us improve both its content and presentation. ...##
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Deterministic subgraph detection in broadcast CONGEST
[article]

2017
*
arXiv
*
pre-print

We present simple deterministic

arXiv:1705.10195v2
fatcat:z56g3wgfpneuldmp4r62ovzw2m
*algorithms**for**subgraph*finding and*enumeration*in the broadcast CONGEST model of distributed computation: --*For*any constant k, detecting k-paths and trees on k nodes ... Moreover, we show that the*algorithms**for*d-degenerate graphs can be improved to optimal complexity O(d/ n) and O(d^2/ n), respectively, in the supported CONGEST model, which can be seen as*an*intermediate ... We thank Juho Hirvonen, Dennis Olivetti, Rotem Oshman, Chris Purcell, Stefan Schmid and Jukka Suomela*for*valuable comments and discussions. ...##
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An algorithmic framework for fixed-cardinality optimization in sparse graphs applied to dense subgraph problems

2015
*
Discrete Applied Mathematics
*

Furthermore, we obtain a fixed-parameter

doi:10.1016/j.dam.2015.04.029
fatcat:jvh3azmuybahri2hudympvvzuq
*algorithm**for*Densest k-*Subgraph**with*respect to the combined parameter "*degeneracy*of G and |V | − k". ... On the negative side, we find that Densest k-*Subgraph*is W[1]-hard*with*respect to the combined parameter "solution size k and*degeneracy*of G". ... We thank Mikko Koivisto*for*pointing out Theorem 1 by Bollobás [8] . References ...##
###
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 ... Indeed, when parameterized by k := vc(G 1 ) + vc(G 2 ) the sum of the vertex cover number of the two input graphs, the problem was shown to be fixed-parameter tractable,*with**an**algorithm*running in time ... We also say that G is the*subgraph*of G*induced*by V . The*degeneracy*of a graph G is the minimum value d*for*which any*induced**subgraph*of G has a vertex*with*degree at most d. ...##
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Computing Dense and Sparse Subgraphs of Weakly Closed Graphs
[article]

2020
*
arXiv
*
pre-print

A graph G is weakly γ-closed if every

arXiv:2007.05630v2
fatcat:woyutwltbzfeflz6yd5j7z4njm
*induced**subgraph*of G contains one vertex v such that*for*each non-neighbor u of v it holds that |N(u)∩ N(v)|<γ. ... Comp. 2020] on clique*enumeration*, we show that several problems related to finding dense*subgraphs*, such as the*enumeration*of bicliques and s-plexes, are fixed-parameter tractable*with*respect to γ(G ...*For*example, there is*an**algorithm*that*enumerates*all maximal cliques of a graph in O(3 d/3 · dn) time and performs very*efficiently*on real-world input instances [9] . ...##
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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. ... Indeed, when parameterized by k := vc(G_1)+vc(G_2) the sum of the vertex cover number of the two input graphs, the problem was shown to be fixed-parameter tractable,*with**an**algorithm*running in time 2 ... As such, it can be used as*an**enumeration**algorithm**for*MCIS. Let us finish this section*with*some general considerations. Note that*for*ISI, the parameter vc + fvs is not the same as fvs + vc. ...
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