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

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*. ...

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

2019
*
International Symposium on Algorithms and Computation
*

The

doi:10.4230/lipics.isaac.2019.63
dblp:conf/isaac/DefrainN19
fatcat:3etthexyhvam3k7zo3qbw5lt2e
*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*. ...##
###
Enumerating Maximal Induced Subgraphs
[article]

2020
*
arXiv
*
pre-print

Given

arXiv:2004.09885v1
fatcat:qibtwqg6izfqdgyfshuhwkx2we
*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. ...##
###
FPT Algorithms for Finding Near-Cliques in c-Closed Graphs
[article]

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*. ...

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

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. ...

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

2017
*
arXiv
*
pre-print

We generalize these ideas to bigger

arXiv:1606.08087v3
fatcat:zkdkbctqdfa5zhk6hz6zlhwkdm
*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. ...##
###
Linear Recognition of Almost Interval Graphs
[article]

2014
*
arXiv
*
pre-print

For any fixed

arXiv:1403.1515v2
fatcat:xeehxn2hmjewlfklfceyeqw2b4
*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. ...##
###
On the Representation of Causal Background Knowledge and its Applications in Causal Inference
[article]

2022
*
arXiv
*
pre-print

The shared directed edges and links

arXiv:2207.05067v1
fatcat:dysv7xmrevdr3eeos65d5zkqzu
*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*. ...##
###
Approximation in (Poly-) Logarithmic Space

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

We also devise

doi:10.4230/lipics.mfcs.2020.16
dblp:conf/mfcs/00010020
fatcat:zlbrpgx7qzdgbbkb5azgzgqocy
*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*. ...##
###
On the Efficiency of Backtracking Algorithms for Binary Constraint Satisfaction Problems

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 ...

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

2015
*
arXiv
*
pre-print

To extract the Markov property, we define an undirected

arXiv:1511.00108v1
fatcat:vqwdnne5yzfxde5cwxqyr4ij6u
*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). ...##
###
Approximation in (Poly-) Logarithmic Space
[article]

2021
*
arXiv
*
pre-print

We also devise

arXiv:2008.04416v2
fatcat:svzkcgvwcze2jocceupnkbcspy
*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*. ...##
###
Graph Isomorphism Restricted by Lists
[article]

2016
*
arXiv
*
pre-print

The complexity

arXiv:1607.03918v2
fatcat:rea4gbmazrbebbirsyhndky7mu
*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 ...##
###
Multiplicity adjustment for temporal and spatial scan statistics using Markov property

2018
*
Japanese Journal of Statistics and Data Science
*

We propose

doi:10.1007/s42081-018-0007-5
fatcat:ok4m2jlnojhu5alupicfc6ptcm
*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*...
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