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The Graph Motif problem parameterized by the structure of the input graph

Édouard Bonnet, Florian Sikora
2017 Discrete Applied Mathematics  
Though, in the many applications of Graph Motif, the input graph originates from real-life and has structure.  ...  The Graph Motif problem was introduced in 2006 in the context of biological networks.  ...  Graph Motif is W[1]-hard with respect to the max leaf number plus the number of colors, even on trees. 322 The 322 Graph Motif Problem Parameterized by the Structure of the Input Graph FPT but no polynomial-size  ... 
doi:10.1016/j.dam.2016.11.016 fatcat:o6mcywvzhncpjmbq76mobqt4ym

Finding approximate and constrained motifs in graphs

Riccardo Dondi, Guillaume Fertin, Stéphane Vialette
2013 Theoretical Computer Science  
Moreover, we show that Min-Substitute is in FPT when parameterized by the size of M.  ...  input graph has diameter 2.  ...  V T of motif M in G, we can compute in polynomial time a solution of Min-SC of size at most k.  ... 
doi:10.1016/j.tcs.2012.08.023 fatcat:pcxu2teffnfkxmginaxdbhdubu

Finding Approximate and Constrained Motifs in Graphs [chapter]

Riccardo Dondi, Guillaume Fertin, Stéphane Vialette
2011 Lecture Notes in Computer Science  
Moreover, we show that Min-Substitute is in FPT when parameterized by the size of M.  ...  input graph has diameter 2.  ...  V T of motif M in G, we can compute in polynomial time a solution of Min-SC of size at most k.  ... 
doi:10.1007/978-3-642-21458-5_33 fatcat:3wklghk4gjdxff3g37lnducpey

Counting Problems in Parameterized Complexity

Radu Curticapean, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
After an introduction to the peculiarities of counting complexity, we survey the parameterized approach to counting problems, with a focus on two topics of recent interest: Counting small patterns in large  ...  graphs, and counting perfect matchings and Hamiltonian cycles in well-structured graphs.  ...  This naturally leads to parameterized pattern counting problems: Given as input a pattern graph H and a host graph G, determine the number of occurrences of H in G, parameterized by the size of H.  ... 
doi:10.4230/lipics.ipec.2018.1 dblp:conf/iwpec/Curticapean18 fatcat:tdfs7zngzrgv5fixf2qawrccuy

Graph Motif Problems Parameterized by Dual

Guillaume Fertin, Christian Komusiewicz
2020 Journal of Graph Algorithms and Applications  
We study the three problems GM, CGM, and LGM, parameterized by := |V | − |M |.  ...  The Colorful Graph Motif (or CGM) problem is the special case of GM in which M is a set, and the List-Colored Graph Motif (or LGM) problem is the extension of GM in which each vertex v of V may choose  ...  Other parameters, essentially related to the structure of the input graph G, have been studied by Bonnet and Sikora [6] .  ... 
doi:10.7155/jgaa.00538 fatcat:h2v2ixkz4nd4fjjogpym3gqcqa

Using Neighborhood Diversity to Solve Hard Problems [article]

Robert Ganian
2012 arXiv   pre-print
Our article further studies this area and provides new algorithms parameterized by neighborhood diversity for the p-Vertex-Disjoint Paths, Graph Motif and Precoloring Extension problems -- the latter two  ...  Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the target graph class.  ...  Our article further develops this direction and provides new algorithms parameterized by neighborhood diversity for the Graph Motif, p-Vertex-Disjoint Paths and Precoloring Extension problems.  ... 
arXiv:1201.3091v2 fatcat:uaa5htjs2bacdng34zmowcfmuy

Improving Vertex Cover as a Graph Parameter

Robert Ganian
2015 Discrete Mathematics & Theoretical Computer Science  
The advantage of twin-cover over vertex cover is that it imposes a lesser restriction on the graph structure and attains low values even on dense graphs.  ...  In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that  ...  This is also the first parameterized algorithm for the problem which only parameterizes the structure of the graph and not M .  ... 
doi:10.46298/dmtcs.2136 fatcat:z3viox6nwvaojc3iibyikwqywu

Graph Motif Problems Parameterized by Dual [article]

Guillaume Fertin, Christian Komusiewicz
2019 arXiv   pre-print
We study the three problems GM, CGM, and LGM, parameterized by the dual parameter ℓ:=|V|-|M|.  ...  The Colorful Graph Motif (or CGM) problem is the special case of GM in which M is a set, and the List-Colored Graph Motif (or LGM) problem is the extension of GM in which each vertex v of V may choose  ...  For example, Graph Motif is fixed-parameter tractable when parameterized by the size of a vertex cover of the input graph [17, 6] .  ... 
arXiv:1908.03870v1 fatcat:gfvvpk36g5ae3gbonafoed6h5y

Guest Editorial: Special Issue on Parameterized and Exact Computation, Part II

Venkatesh Raman, Saket Saurabh
2013 Algorithmica  
However the paper shows that when the vertex cover number of the corresponding graph is a small parameter, these problems can be solved in space which is polynomial in the input size (with a super polynomial  ...  While some of the papers in this volume supplement the ones in the first volume in the sub areas of kernelization and improved fixed-parameter algorithms for graph modification problems, most others complement  ...  The paper gives new improved fixed-parameter algorithms for Graph Motif problem and some of its variants.  ... 
doi:10.1007/s00453-013-9744-9 fatcat:j2ya4p5u7zcvlgvxwotywr7f34

Kernelization Hardness of Connectivity Problems in d-Degenerate Graphs [chapter]

Marek Cygan, Marcin Pilipczuk, Michał Pilipczuk, Jakub Onufry Wojtaszczyk
2010 Lecture Notes in Computer Science  
Inspired by recent work by Philip, Raman and Sikdar, who have shown the existence of a polynomial kernel for DOMINATING SET in d-degenerate graphs, we investigate kernelization hardness of problems that  ...  We prove this using a problem originated from bioinformatics -COLOURFUL GRAPH MOTIF -analyzed and proved to be NP-hard by Fellows et al.  ...  Whenever we speak of a parameterized problem Q, by d-deg-Q we denote the problem Q, where the class of input graphs is restricted to d-degenerate graphs.  ... 
doi:10.1007/978-3-642-16926-7_15 fatcat:irxbf2eapzaexa52bghnohykha

Parameterized Explainer for Graph Neural Network [article]

Dongsheng Luo, Wei Cheng, Dongkuan Xu, Wenchao Yu, Bo Zong, Haifeng Chen, Xiang Zhang
2020 arXiv   pre-print
Despite recent progress in Graph Neural Networks (GNNs), explaining predictions made by GNNs remains a challenging open problem.  ...  PGExplainer adopts a deep neural network to parameterize the generation process of explanations, which enables PGExplainer a natural approach to explaining multiple instances collectively.  ...  First, PGExplainer learns a latent variable for each edge in the original input graph with a neural network parameterized by Ψ, which is shared by all edges in the population of input graphs.  ... 
arXiv:2011.04573v1 fatcat:afunqbkdhvht5brvy5uqiozlq4

Optimality and tight results in parameterized complexity (Dagstuhl Seminar 14451)

Stefan Kratsch, Daniel Lokshtanov, Dániel Marx, Peter Rossmanith, Marc Herbstritt
2015 Dagstuhl Reports  
Over the last two decades parameterized complexity has become one of the main tools for handling intractable problems.  ...  The report contains the abstracts of the results presented at the seminar, as well as a collection of open problems stated at the seminar.  ...  We also consider the List-Colored Graph Motif problem. In this extension of Graph Motif each vertex may choose its color from a list of colors.  ... 
doi:10.4230/dagrep.4.11.1 dblp:journals/dagstuhl-reports/KratschLMR14 fatcat:vwgmhttkgrf4pb34jpsb2rfvnm

Upper and lower bounds for finding connected motifs in vertex-colored graphs

Michael R. Fellows, Guillaume Fertin, Danny Hermelin, Stéphane Vialette
2011 Journal of computer and system sciences (Print)  
We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors  ...  This problem is a natural graph-theoretic pattern matching variant where we are not interested in the actual structure of the occurrence of the pattern, we only require it to preserve the very basic topological  ...  In particular, we are interested in investigating Graph Motif under different parameters governing the structure of the input.  ... 
doi:10.1016/j.jcss.2010.07.003 fatcat:7gxef3njs5g5joy7emu4blph4u

Kernelization hardness of connectivity problems in d-degenerate graphs

Marek Cygan, Marcin Pilipczuk, Michał Pilipczuk, Jakub Onufry Wojtaszczyk
2012 Discrete Applied Mathematics  
Inspired by the recent work by Philip, Raman and Sikdar, who have shown the existence of a polynomial kernel for Dominating Set in d-degenerate graphs, we investigate the kernelization complexity of problems  ...  We prove this using a problem that originates from bioinformatics -Colourful Graph Motif -analysed and proved to be NP-hard by Fellows et al.  ...  What about H-topological-minor-free graphs? To the best of our knowledge, these three problems cannot be easily covered by the recent results of Langer et al. [27] .  ... 
doi:10.1016/j.dam.2012.05.016 fatcat:xwx5p5lgvnebndqjkng56czfe4

A Systematic Survey on Deep Generative Models for Graph Generation [article]

Xiaojie Guo, Liang Zhao
2020 arXiv   pre-print
As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs.  ...  This article provides an extensive overview of the literature in the field of deep generative models for the graph generation.  ...  [105] also deal with the molecule generation problem but with a different way of defining the graph motifs.  ... 
arXiv:2007.06686v2 fatcat:xox7apwdvbfhlgnsgrr3w3rv5m
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