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

Kunihiro Wasa, Hiroki Arimura, Takeaki Uno
2014 Lecture Notes in Computer Science  
In this paper, we address the problem of 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.  ... 
doi:10.1007/978-3-319-13075-0_8 fatcat:5elaatgm2zbddlvmvrkmnxreyu

Efficient Exact Algorithms for Maximum Balanced Biclique Search in Bipartite Graphs [article]

Lu Chen, Chengfei Liu, Rui Zhou, Jiajie Xu, Jianxin Li
2020 arXiv   pre-print
To further speed up this 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  ... 
arXiv:2007.08836v1 fatcat:dkfq624d6vfb5lzgpqcy5yxgc4

FPT Algorithms for Finding Near-Cliques in c-Closed Graphs [article]

Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, C. Seshadhri
2021 arXiv   pre-print
We study various established notions of such substructures, including k-plexes, complements of 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.  ... 
arXiv:2007.09768v4 fatcat:z6eu4ca7orez5cdiexwavuzgg4

An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs [article]

Kazuhiro Kurita and Kunihiro Wasa and Hiroki Arimura and Takeaki Uno
2019 arXiv   pre-print
In this paper, we propose a characterization of chordal bipartite graphs and 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.  ... 
arXiv:1903.02161v1 fatcat:dsgsp66xuneaxfzaotnsp3e44e

Efficient Enumeration of Bipartite Subgraphs in Graphs [chapter]

Kunihiro Wasa, Takeaki Uno
2018 Lecture Notes in Computer Science  
As the main results, we develop two 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.  ... 
doi:10.1007/978-3-319-94776-1_38 fatcat:xr6pgqjd3bhmdcy2adnq3nqkgu

Finding Dense Subgraphs of Sparse Graphs [chapter]

Christian Komusiewicz, Manuel Sorge
2012 Lecture Notes in Computer Science  
Furthermore, we obtain a fixedparameter 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.  ... 
doi:10.1007/978-3-642-33293-7_23 fatcat:utinw4vbsfd3nhuxkikvbvxqhi

Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six

Suman K. Bera, Noujan Pashanasangi, C. Seshadhri, Michael Wagner
2020 Innovations in Theoretical Computer Science  
Our main theorem asserts linear time 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.)  ... 
doi:10.4230/lipics.itcs.2020.38 dblp:conf/innovations/BeraPS20 fatcat:crkyagghbzbcfh3gvd7qoy4esq

Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six [article]

Suman K. Bera, Noujan Pashanasangi, C. Seshadhri
2019 arXiv   pre-print
In a classic result, Chiba and Nishizeki (SICOMP 85) gave linear time 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.  ... 
arXiv:1911.05896v2 fatcat:ftxidoc4m5arhe53r44pu546qi

Scaling Up Maximal k-plex Enumeration [article]

Qiangqiang Dai, Rong-Hua Li, Hongchao Qin, Meihao Liao, Guoren Wang
2022 arXiv   pre-print
Then, we develop a new branch-and-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 ( ) = {( , )|( , ) ∈ , ∈ , ∈ }.  ... 
arXiv:2203.10760v3 fatcat:7zpmmysp2za33ezzn6c7xijt4i

Proximity Search For Maximal Subgraph Enumeration [article]

Alessio Conte, Andrea Marino, Roberto Grossi, Takeaki Uno, Luca Versari
2021 arXiv   pre-print
Bipartite 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.  ... 
arXiv:1912.13446v3 fatcat:aiwlhrezcjbyrelpcxe45jb7zu

Deterministic subgraph detection in broadcast CONGEST [article]

Janne H. Korhonen, Joel Rybicki
2017 arXiv   pre-print
We present simple deterministic 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.  ... 
arXiv:1705.10195v2 fatcat:z56g3wgfpneuldmp4r62ovzw2m

An algorithmic framework for fixed-cardinality optimization in sparse graphs applied to dense subgraph problems

Christian Komusiewicz, Manuel Sorge
2015 Discrete Applied Mathematics  
Furthermore, we obtain a fixed-parameter 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  ... 
doi:10.1016/j.dam.2015.04.029 fatcat:jvh3azmuybahri2hudympvvzuq

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  ...  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.  ... 
doi:10.1007/978-3-319-19315-1_1 fatcat:knzdi3nve5ao7kvxr7ubulpdnq

Computing Dense and Sparse Subgraphs of Weakly Closed Graphs [article]

Tomohiro Koana, Christian Komusiewicz, Frank Sommer
2020 arXiv   pre-print
A graph G is weakly γ-closed if every 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] .  ... 
arXiv:2007.05630v2 fatcat:woyutwltbzfeflz6yd5j7z4njm

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.  ...  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.  ... 
arXiv:1412.1261v2 fatcat:ownbquhznvcrnmz4uthnys5o3m
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