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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

Efficient enumeration of maximal split subgraphs and sub-cographs and related classes [article]

Caroline Brosse, Aurélie Lagoutte, Vincent Limouzy, Arnaud Mary, Lucas Pastor
2020 arXiv   pre-print
In this paper, we are interested in algorithms that take in input an arbitrary graph G, and that enumerate in output all the (inclusion-wise) maximal "subgraphs" of G which fulfil a given property Π.  ...  More precisely, we present efficient algorithms to list all maximal split subgraphs, sub-cographs and some subclasses of cographs of a given input graph.  ...  [8, 9] considered several graph classes such as maximal chordal graphs, maximal bipartite graphs, or maximal k-degenerate graphs inside an arbitrary graph.  ... 
arXiv:2007.01031v1 fatcat:rvub4qkhjnbxzdpofw4qjps55m

Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7 - Free and P_8 - Free Chordal Graphs

Oscar Defrain, Lhouari Nourine, Michael Wagner
2019 International Symposium on Algorithms and Computation  
The subgraph of An induced path (resp. induced cycle) in G is a path (resp. cycle) that is an induced subgraph of G. We denote by P k an induced path on k vertices.  ...  In this paper, we investigate generalizations of this technique to P k -free chordal graphs for larger integers k.  ...  The next theorem suggests that the enumeration of D RN (G) is tractable in P 7 -free and P 8 -free chordal graphs. Proposition 5. Let G be a chordal graph.  ... 
doi:10.4230/lipics.isaac.2019.63 dblp:conf/isaac/DefrainN19 fatcat:3etthexyhvam3k7zo3qbw5lt2e

Enumerating Maximal Induced Subgraphs [article]

Yixin Cao
2020 arXiv   pre-print
Given a graph G, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of G that belong to a certain hereditary graph class.  ...  A general technique that has been proved very powerful in enumeration algorithms is to build a solution map, i.e., a multiple digraph on all the solutions of the problem, and the key of this approach is  ...  The author would like to thank Mamadou Moustapha Kanté for bringing Theorem 5.2 of [25] (part of Corollary 1.5) to our attention, and for very helpful comments on an early version of the paper.  ... 
arXiv:2004.09885v1 fatcat:qibtwqg6izfqdgyfshuhwkx2we

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
In this work, we prove that many different kinds of maximal near-cliques can be enumerated in polynomial time (and FPT in c) for c-closed graphs.  ...  (SICOMP 2020) introduced the notion of c-closed graphs and proved that maximal clique enumeration is fixed-parameter tractable with respect to c.  ...  Moreover, we use this result to show that maximal bounded co-degenerate subgraphs can be enumerated efficiently.  ... 
arXiv:2007.09768v4 fatcat:z6eu4ca7orez5cdiexwavuzgg4

Neighborhood inclusions for minimal dominating sets enumeration: linear and polynomial delay algorithms in P_7-free and P_8-free chordal graphs [article]

Oscar Defrain, Lhouari Nourine
2019 arXiv   pre-print
In this paper, we investigate generalizations of this technique to P_k-free chordal graphs for larger integers k.  ...  As for P_k-free chordal graphs for k≥ 9, we give evidence that such a technique is inefficient as a key step of the algorithm, namely the irredundant extension problem, becomes NP-complete.  ...  Neighborhood inclusions for minimal dominating sets enumeration all the clauses, and D the associated set of vertices in G. By construction D dominates all the c i 's.  ... 
arXiv:1805.02412v2 fatcat:yvlfpi42snbahgvcuoukzgdmj4

A width parameter useful for chordal and co-comparability graphs [article]

Dong Yeap Kang, O-joung Kwon, Torstein J.F. Strømme, Jan Arne Telle
2017 arXiv   pre-print
We generalize these ideas to bigger graph classes. We introduce a new width parameter sim-width, of stronger modelling power than mim-width, by making a small change in the definition of mim-width.  ...  We investigate a way to bound mim-width for graphs of bounded sim-width by excluding K_t K_t and K_t S_t as induced minors or induced subgraphs, and give algorithmic consequences.  ...  We investigate a way to bound mim-width for graphs of bounded sim-width by excluding K t K t and K t S t as induced minors or induced subgraphs, and give algorithmic consequences.  ... 
arXiv:1606.08087v3 fatcat:zkdkbctqdfa5zhk6hz6zlhwkdm

Linear Recognition of Almost Interval Graphs [article]

Yixin Cao
2014 arXiv   pre-print
For any fixed k, we give linear-time algorithms for recognizing all these classes, and in the case of membership, our algorithms provide also a specific interval graph as evidence.  ...  Moreover, our algorithms for recognizing interval+ k v and interval- k e run in times O(6^k · (n + m)) and O(8^k · (n + m)), (where n and m stand for the numbers of vertices and edges respectively in the  ...  I am indebted to Sylvain Guillemot and Yang Liu for careful reading of an early version of this manuscript and their penetrating criticism.  ... 
arXiv:1403.1515v2 fatcat:xeehxn2hmjewlfklfceyeqw2b4

On the Representation of Causal Background Knowledge and its Applications in Causal Inference [article]

Zhuangyan Fang, Ruiqi Zhao, Yue Liu, Yangbo He
2022 arXiv   pre-print
The shared directed edges and links of a subclass of Markov equivalent DAGs refined due to background knowledge can be represented by a causal maximally partially directed acyclic graph (MPDAG).  ...  In this paper, we first provide a sound and complete graphical characterization of causal MPDAGs and give a minimal representation of a causal MPDAG.  ...  A clique is called maximal if it is not a proper subset of any other cliques. Let C be a chordal graph over vertex set V(C). Any induced subgraph of C is chordal.  ... 
arXiv:2207.05067v1 fatcat:dysv7xmrevdr3eeos65d5zkqzu

Approximation in (Poly-) Logarithmic Space

Arindam Biswas, Venkatesh Raman, Saket Saurabh, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
We also devise a factor-O(d²) approximation algorithm for Dominating Set on d-degenerate graphs which runs in time n^{O(log n)} and uses O(log² n) bits of space.  ...  For Independent Set on graphs with average degree d, we give a factor-(2d) approximation algorithm which runs in polynomial time and uses O(log n) bits of space.  ...  Graphs of Bounded Degeneracy A graph is called d-degenerate if there is a vertex of degree at most d in every subgraph of G. A graph with maximum degree d is clearly d-degenerate.  ... 
doi:10.4230/lipics.mfcs.2020.16 dblp:conf/mfcs/00010020 fatcat:zlbrpgx7qzdgbbkb5azgzgqocy

On the Efficiency of Backtracking Algorithms for Binary Constraint Satisfaction Problems

Achref El Mouelhi, Philippe Jégou, Cyril Terrioux, Bruno Zanuttini
2012 International Symposium on Artificial Intelligence and Mathematics  
In this paper, we address the issue of tractable classes of CSPs from a different perspective.  ...  By relating the complexity of CSP algorithms to graph-theoretic parameters, our analysis allows us to point at new tractable classes, which can be solved directly by the usual CSP algorithms in polynomial  ...  Acknowledgments Philippe Jégou would like to thank Maria Chudnowsky for their fruitful discussion, about graphs theory, perfect graphs and links with classes of graphs related to the clique problem, and  ... 
dblp:conf/isaim/MouelhiJTZ12 fatcat:fjqr6zezvvcnnk2qtsg7s3eede

Recursive computation for evaluating the exact p-values of temporal and spatial scan statistics [article]

Satoshi Kuriki, Kunihiko Takahashi, Hisayuki Hara
2015 arXiv   pre-print
To extract the Markov property, we define an undirected graph whose cliques are B_j, and obtain its chordal extension, from which we present the expressions of the recursive formula.  ...  This problem is motivated from the evaluation of the multiplicity-adjusted p-value of scan statistics in spatial epidemiology.  ...  −1 (5) = {3, 4}, k −1 Chordal graph G (left: added edges are in red, right: maximal cliques are in green).  ... 
arXiv:1511.00108v1 fatcat:vqwdnne5yzfxde5cwxqyr4ij6u

Approximation in (Poly-) Logarithmic Space [article]

Arindam Biswas and Venkatesh Raman and Saket Saurabh
2021 arXiv   pre-print
We also devise a factor-O(d^2) approximation algorithm for Dominating Set on d-degenerate graphs which runs in time n^O(log n) and uses O(log^2 n) bits of space.  ...  We devise a factor-2 approximation algorithm for Vertex Cover on graphs with maximum degree Δ, and an algorithm for computing maximal independent sets which both run in time n^O(Δ) and use O(Δlog n) bits  ...  Graphs of Bounded Degeneracy A graph is called d-degenerate if there is a vertex of degree at most d in every subgraph of G. A graph with maximum degree d is clearly d-degenerate.  ... 
arXiv:2008.04416v2 fatcat:svzkcgvwcze2jocceupnkbcspy

Graph Isomorphism Restricted by Lists [article]

Pavel Klavik, Dušan Knop, Peter Zeman
2016 arXiv   pre-print
The complexity of graph isomorphism (GraphIso) is a famous unresolved problem in theoretical computer science. For graphs G and H, it asks whether they are the same up to a relabeling of vertices.  ...  In 1981, Lubiw proved that list restricted graph isomorphism (ListIso) is NP-complete: for each u ∈ V(G), we are given a list L(u) ⊆ V(H) of possible images of u.  ...  Unfortunately, no purely combinatorial description of the results is available, and we believe that such a description of a combinatorial algorithm for solving graph isomorphism of graphs with excluded  ... 
arXiv:1607.03918v2 fatcat:rea4gbmazrbebbirsyhndky7mu

Multiplicity adjustment for temporal and spatial scan statistics using Markov property

Satoshi Kuriki, Kunihiko Takahashi, Hisayuki Hara
2018 Japanese Journal of Statistics and Data Science  
We propose a recursive summation/integration technique using the Markov property, which is extracted from a chordal graph defined by temporal and spatial structures.  ...  We discuss computation of the conditional expectation in a multinomial distribution.  ...  Step 1: Constructing a chordal extension and enumerating maximal cliques In this step, we add edges of E 1 to G, so that the extended graph e G ¼ ðV; E [ E 1 Þ is a chordal graph and we find all maximal  ... 
doi:10.1007/s42081-018-0007-5 fatcat:ok4m2jlnojhu5alupicfc6ptcm
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