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A Parametrized Analysis of Algorithms on Hierarchical Graphs
[chapter]

2017
*
Lecture Notes in Computer Science
*

(3) We handle

doi:10.1007/978-3-319-60252-3_9
fatcat:vlnovsvmtna23g2tgdgmgb2nii
*labeled*hierarchical*graphs*, where edges are*labeled*by letters from some alphabet, and the*problems*refer to the languages of the*graphs*. ... complexity*in*the hierarchical*setting*. ... An application:*Constrained**shortest**path*The*problem*of finding the*shortest**labeled**path*is to find, given*a**labeled*weighted*graph*G = V, s, T, E, w, Σ, l and*a*DFA*A*= Σ, Q, q 0 , δ, F , the*shortest*...##
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Adding regular expressions to graph reachability and pattern queries

2011
*
2011 IEEE 27th International Conference on Data Engineering
*

For such

doi:10.1109/icde.2011.5767858
dblp:conf/icde/FanLMTW11
fatcat:gpmvdy7z3zdjzkpx4bpjadg4ry
*graphs*we propose*a*class of reachability queries and*a*class of*graph*patterns,*in*which an edge is specified with*a*regular expression of*a*certain form, expressing the connectivity*in**a*data ...*In*addition, we define*graph*pattern matching based on*a*revised notion of*graph*simulation. ... Fan, Ma and and Wu are supported*in*part by EPSRC E029213/1. Li is supported*in*part by the Key Program of NSFC 61033015. ...##
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Contraction decomposition in h-minor-free graphs and algorithmic applications

2011
*
Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
*

We prove that any

doi:10.1145/1993636.1993696
dblp:conf/stoc/DemaineHK11
fatcat:t47inb45ubbuhjaok46ikjqsqa
*graph*excluding*a*fixed minor can have its edges partitioned into*a*desired number k of*color*classes such that contracting the edges*in*any one*color*class results*in**a**graph*of treewidth ...*set*of vertices instead of just one, as long as this*set*is tight*in**a*certain sense. ... This decomposition*approach*has been successfully used to obtain constantfactor approximations for many*graph**problems*, such as*a*2approximation for*graph**coloring**in*any odd-H-minor-free*graph*family ...##
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Interval Graphs: Canonical Representations in Logspace

2011
*
SIAM journal on computing (Print)
*

This

doi:10.1137/10080395x
fatcat:jz7pe4spa5hxbf46vx4gx7ephe
*approach*also yields*a*canonical*labeling*of convex*graphs*. As*a*consequence, the isomorphism and automorphism*problems*for these*graph*classes are solvable*in*logspace. ... We present*a*logspace algorithm for computing*a*canonical*labeling*,*in*fact*a*canonical interval representation, for interval*graphs*. ... Let B 0 · · · B k be*a**shortest*overlap-*path**in*O such that S ⊆ B 0 and B k contains precisely one of u and v. The claim is proved by induction on the length k of the*path*. ...##
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Efficient parallel algorithms for chordal graphs

1988
*
[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
*

We give the first efficient parallel algorithms for recognizing chordal

doi:10.1109/sfcs.1988.21933
dblp:conf/focs/Klein88
fatcat:cdmk6ju75rbdfbxfcymexdrgwy
*graphs*, finding*a*maximum clique and*a*maximum independent*set**in**a*chordal*graph*, finding an optimal*coloring*of*a*chordal*graph*... Thus they identified*problem*2 as*a*bottleneck*in*analyzing chordal*graphs*. ... Many thanks to David Shmoys, who advised the thesis based*in*part on this research. ...##
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Algebraic Property Graphs
[article]

2020
*
arXiv
*
pre-print

*In*this paper, we observe that algebraic data types are

*a*common foundation of most of the enterprise schema languages we deal with

*in*practice, and are also

*a*suitable basis for

*a*property

*graph*formalism ... One of the main challenges of building an enterprise knowledge

*graph*is guaranteeing interoperability between

*a*single

*graph*data model and the diverse and often changeable ecosystem of non-

*graph*data ... Acknowledgements We would particularly like to thank Jan Hidders for contributing

*a*

*set*-based formalism which aligns APG with the emerging property

*graph*standard, and we expect to revisit this model when ...

##
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DDGK: Learning Graph Representations for Deep Divergence Graph Kernels

2019
*
The World Wide Web Conference on - WWW '19
*

*In*this paper, we show that it is possible to learn representations for

*graph*similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or

*labeled*

*graphs*). ... This

*approach*, which we call isomorphism attention, captures how well the representations of one

*graph*can encode another. ...

*In*supervised

*graph*classification, the task is to solve an endto-end whole-

*graph*classification

*problem*(i.e. the

*problem*of assigning

*a*

*label*to the entire

*graph*). ...

##
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Knowledge Graph Reasoning with Relational Directed Graph
[article]

2021
*
arXiv
*
pre-print

*In*this paper, we introduce

*a*novel relational structure, i.e., relational directed

*graph*(r-digraph), which is composed of overlapped relational

*paths*, to capture the KG's structural information. ... Methods based on the relational

*path*

*in*the literature have shown strong, interpretable, and inductive reasoning ability. However, the

*paths*are naturally limited

*in*capturing complex topology

*in*KG. ...

*In*this way, they can be formed as

*paths*

*in*

*a*layered st-

*graph*, with the single source entity e q and single sink entity e

*a*. ...

##
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Graph mining

2006
*
ACM Computing Surveys
*

Indeed, any M : N relation

doi:10.1145/1132952.1132954
fatcat:jbc67scdzbe4vj5o5fjerdy6xq
*in*database terminology can be represented as*a**graph*.*A*lot of these questions boil down to the following: "How can we generate synthetic but realistic*graphs*?" ... To answer this, we must first understand what patterns are common*in*real-world*graphs*and can thus be considered*a*mark of normality/realism. ... Consider all*shortest**paths*between all pairs of nodes*in**a**graph*. The edge-betweenness or stress of an edge is the number of these*shortest**paths*that the edge belongs to. ...##
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Adding regular expressions to graph reachability and pattern queries

2012
*
Frontiers of Computer Science
*

*In*addition, we define

*graph*pattern matching based on

*a*revised notion of

*graph*simulation. ... For such

*graphs*we propose

*a*class of reachability queries and

*a*class of

*graph*patterns,

*in*which an edge is specified with

*a*regular expression of

*a*certain form, expressing the connectivity of

*a*data ... One follows

*a*join-based

*approach*, while the other adopts

*a*split-based

*approach*commonly used

*in*

*labeled*transition systems. ...

##
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Graph Cuts with Interacting Edge Costs - Examples, Approximations, and Algorithms
[article]

2016
*
arXiv
*
pre-print

We study an extension of the classical

arXiv:1402.0240v4
fatcat:wznkbacpcnashntirqnv5z24um
*graph*cut*problem*, wherein we replace the modular (sum of edge weights) cost function by*a*submodular*set*function defined over*graph*edges. ... Special cases of this*problem*have appeared*in*different applications*in*signal processing, machine learning, and computer vision. ... Our instance is*a**graph*with n = 10 modes, shown*in*Figure 6 . The*graph*edges are partitioned into n/2*sets*, indicated by*colors*. ...##
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Quegel: A General-Purpose Query-Centric Framework for Querying Big Graphs
[article]

2016
*
arXiv
*
pre-print

*In*this work, we develop

*a*new open-source system, called Quegel, for querying big

*graphs*, which treats queries as first-class citizens

*in*the design of its computing model. ... The programming paradigm adopted by these systems can seriously under-utilize the resources

*in*

*a*cluster for

*graph*query processing. ... Now the

*problem*of computing P2P

*shortest*

*path*over the terrain is transformed to the

*problem*of computing the P2P

*shortest*

*path*

*in*the transformed network. ...

##
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Online Graph Dictionary Learning
[article]

2021
*
arXiv
*
pre-print

Our

arXiv:2102.06555v2
fatcat:eqg6e7s3lrfe5g5uuihpryjhwq
*approach*naturally extends to*labeled**graphs*, and is completed by*a*novel upper bound that can be used as*a*fast approximation of Gromov Wasserstein*in*the embedding space. ... We fill this gap by proposing*a*new online*Graph*Dictionary Learning*approach*, which uses the Gromov Wasserstein divergence for the data fitting term. ... As the proper*graph*representations for OT-based methods is still*a*question of key interest, we consistently benchmarked our*approach*and these kernels when we consider adjacency and*shortest*-*path*representations ...##
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Recent Advances in Graph Partitioning
[article]

2015
*
arXiv
*
pre-print

We survey recent trends

arXiv:1311.3144v3
fatcat:zmvhlkh7ynbzvm353fv22f2gnq
*in*practical algorithms for balanced*graph*partitioning together with applications and future research directions. ... Acknowledgements We express our gratitude to Bruce Hendrickson, Dominique LaSalle, and George Karypis for many valuable comments on*a*preliminary draft of the manuscript. ... For example, KaHIP [SS] uses weighted matching, spanning trees, edge*coloring*, BFS,*shortest**paths*, diffusion, maximum flows, and strongly connected components. ...##
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A SURVEY OF PROGRESS IN GRAPH THEORY IN THE SOVIET UNION

1970
*
Annals of the New York Academy of Sciences
*

This report describes the results of

doi:10.1111/j.1749-6632.1970.tb56496.x
fatcat:cbb5x22w2farrnw5sijyovn66i
*a*comprehensive technical survey of all published Soviet literature*in**graph*theory and its applications--more than 230 technical articles appearing up to June 1968 ... use of*graphs*for modeling*in*social sciences. ... ) standard*shortest*-*path**problems*, and (3) Two*labelling*algorithms are given for constructing*a*relief of*a**graph*. ...
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