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A Parametrized Analysis of Algorithms on Hierarchical Graphs [chapter]

Rachel Faran, Orna Kupferman
2017 Lecture Notes in Computer Science  
(3) We handle 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  ... 
doi:10.1007/978-3-319-60252-3_9 fatcat:vlnovsvmtna23g2tgdgmgb2nii

Adding regular expressions to graph reachability and pattern queries

Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, Yinghui Wu
2011 2011 IEEE 27th International Conference on Data Engineering  
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 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.  ... 
doi:10.1109/icde.2011.5767858 dblp:conf/icde/FanLMTW11 fatcat:gpmvdy7z3zdjzkpx4bpjadg4ry

Contraction decomposition in h-minor-free graphs and algorithmic applications

Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ichi Kawarabayashi
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
We prove that any 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  ... 
doi:10.1145/1993636.1993696 dblp:conf/stoc/DemaineHK11 fatcat:t47inb45ubbuhjaok46ikjqsqa

Interval Graphs: Canonical Representations in Logspace

Johannes Köbler, Sebastian Kuhnert, Bastian Laubner, Oleg Verbitsky
2011 SIAM journal on computing (Print)  
This 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.  ... 
doi:10.1137/10080395x fatcat:jz7pe4spa5hxbf46vx4gx7ephe

Efficient parallel algorithms for chordal graphs

P.N. Klein
1988 [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science  
We give the first efficient parallel algorithms for recognizing chordal 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.  ... 
doi:10.1109/sfcs.1988.21933 dblp:conf/focs/Klein88 fatcat:cdmk6ju75rbdfbxfcymexdrgwy

Algebraic Property Graphs [article]

Joshua Shinavier, Ryan Wisnesky
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  ... 
arXiv:1909.04881v2 fatcat:qvpjn36v6zfl5obueylat67bhm

DDGK: Learning Graph Representations for Deep Divergence Graph Kernels

Rami Al-Rfou, Bryan Perozzi, Dustin Zelle
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).  ... 
doi:10.1145/3308558.3313668 dblp:conf/www/Al-RfouPZ19 fatcat:mhhomms6uffrvlvbfb5u62eire

Knowledge Graph Reasoning with Relational Directed Graph [article]

Yongqi Zhang, Quanming Yao
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 .  ... 
arXiv:2108.06040v1 fatcat:55ej2pco2jc5jca6tsg4mvoavm

Graph mining

Deepayan Chakrabarti, Christos Faloutsos
2006 ACM Computing Surveys  
Indeed, any M : N relation 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.  ... 
doi:10.1145/1132952.1132954 fatcat:jbc67scdzbe4vj5o5fjerdy6xq

Adding regular expressions to graph reachability and pattern queries

Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, Yinghui Wu
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.  ... 
doi:10.1007/s11704-012-1312-y fatcat:nbgfluc3cfdkvjrqkkdbh3d7wi

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

Stefanie Jegelka
2016 arXiv   pre-print
We study an extension of the classical 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.  ... 
arXiv:1402.0240v4 fatcat:wznkbacpcnashntirqnv5z24um

Quegel: A General-Purpose Query-Centric Framework for Querying Big Graphs [article]

Da Yan, James Cheng, M. Tamer Özsu, Fan Yang, Yi Lu, John C.S. Lui, Qizhen Zhang, Wilfred Ng
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.  ... 
arXiv:1601.06497v1 fatcat:ca3bf6cqtbbplnrgmgufb5czbi

Online Graph Dictionary Learning [article]

Cédric Vincent-Cuaz, Titouan Vayer, Rémi Flamary, Marco Corneli, Nicolas Courty
2021 arXiv   pre-print
Our 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  ... 
arXiv:2102.06555v2 fatcat:eqg6e7s3lrfe5g5uuihpryjhwq

Recent Advances in Graph Partitioning [article]

Aydin Buluc, Henning Meyerhenke, Ilya Safro, Peter Sanders, Christian Schulz
2015 arXiv   pre-print
We survey recent trends 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.  ... 
arXiv:1311.3144v3 fatcat:zmvhlkh7ynbzvm353fv22f2gnq


James Turner, William H. Kautz
1970 Annals of the New York Academy of Sciences  
This report describes the results of 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.  ... 
doi:10.1111/j.1749-6632.1970.tb56496.x fatcat:cbb5x22w2farrnw5sijyovn66i
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