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All-Pairs Shortest-Paths for Large Graphs on the GPU [article]

Gary J. Katz, Joseph T. Kider Jr.
2008 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware - HWWS '04  
We describe a shared memory cache efficient GPU implementation to solve transitive closure and the all-pairs shortest-path problem on directed graphs for large datasets.  ...  Experiments demonstrate that our method is able to significantly increase processing large graphs making our method applicable for bioinformatics, internet node traffic, social networking, and routing  ...  The authors would like to thank Norm Badler, Alla Safonova, and Amy Calhoon for all their insightful help.  ... 
doi:10.2312/eggh/eggh08/047-055 fatcat:2g54edmqqrfdbmwtsqsbjvac6u

Parallel cache-efficient code for computing the McCaskill partition functions

Marek Pałkowski, Włodzimierz Bielecki
2019 Proceedings of the 2019 Federated Conference on Computer Science and Information Systems  
A TRACO tiling strategy uses the transitive closure of a dependence graph to avoid affine function calculation. The ISL scheduler is used to parallelize tiled loop nests.  ...  An experimental study carried out on a multi-core computer demonstrates considerable speed-up of generated code for the larger number of threads.  ...  So, a special algorithm should be applied to calculate the transitive closure of a parametric dependence graph.  ... 
doi:10.15439/2019f8 dblp:conf/fedcsis/PalkowskiB19 fatcat:ng45r6gvrrcdpgzbre6vqa46ti

An interval-based temporal algebra based on binary encoding of point relations

Vincent J. Kovarik, Avelino J. Gonzalez
2000 International Journal of Intelligent Systems  
The small memory footprint for the bit-code, the algorithmic transitive relation calculation, and the closure algorithm, together, form an efficient method for providing machine-based temporal reasoning  ...  Also presented is a matrix multiplication algorithm for computing transitive relations based on the definition of sum and product operations for the bit-encoded relation signatures.  ...  This algebraic algorithm for transitive relation calculation then formed the basis for a transitive closure algorithm which computed the closure of a temporal system matrix in O(n 3 ) at the worst case  ... 
doi:10.1002/(sici)1098-111x(200006)15:6<495::aid-int2>;2-c fatcat:4jdaquqsf5eupbtu274u7j73oq

Efficient parallel algorithms for functional dependency manipulations

Radhakrishnan Sridhar, Sitharama S. Iyengar
1990 Proceedings of the second international symposium on Databases in parallel and distributed systems - DPDS '90  
The algorithms are efficient based on the transitive closure bottleneck phenomenon [7] that is, any improvement in the time and processor complexity of the transitive closure algorithm will result in an  ...  We present NC algorithms to obtain a non-redundant and a LR-Minimum cover for the set of functional dependencies Z.  ...  ACKNOWLEDGEMENTS We thank the anonymous refrees for their comments and Dr. Rakesh Agarwal for the prompt communications with respect to our submission to this conference.  ... 
doi:10.1145/319057.319078 fatcat:ixspdmcyn5ew5owjnqtdtluj34

Transitive Closure of a Union of Dependence Relations for Parameterized Perfectly-Nested Loops [chapter]

Włodzimierz Bielecki, Krzysztof Kraska, Tomasz Klimek
2013 Lecture Notes in Computer Science  
This allows us to effectively extract both fine-and coarse-grained parallelism in loops using techniques based on applying the transitive closure of dependence relations.  ...  This paper presents a new approach for computing the transitive closure of a union of relations describing all the dependences in both uniform and quasi-uniform perfectly-nested parameterized loops.  ...  This allows us to extract efficiently both fine-and coarse-grained parallelism in perfectly-nested loops by means of well-known techniques based on applying the transitive closure of dependence relations  ... 
doi:10.1007/978-3-642-39958-9_4 fatcat:yhsbahxwwjg5tnat6kkaebkzlq

One Algorithm to Evaluate Them All: Unified Linear Algebra Based Approach to Evaluate Both Regular and Context-Free Path Queries [article]

Ekaterina Shemetova, Rustam Azimov, Egor Orachev, Ilya Epelbaum, Semyon Grigorev
2021 arXiv   pre-print
Thus, we provide the alternative way to construct a slightly subcubic algorithm for CFPQ which is based on linear algebra and incremental transitive closure (a classic graph-theoretic problem), as opposed  ...  The Kronecker product-based algorithm for context-free path querying (CFPQ) was proposed by Orachev et al. (2020).  ...  Acknowledgements We are grateful to Ekaterina Verbitskaia for careful reading and pointing out some mistakes.  ... 
arXiv:2103.14688v1 fatcat:fy73vloj5zcmjbbwis37rbexte

Transitive closure and metric inequality of weighted graphs: detecting protein interaction modules using cliques

Chris Ding, Xiaofeng He, Hui Xiong, Hanchuan Peng, Stephen R. Holbrook
2006 International Journal of Data Mining and Bioinformatics  
This can be used to define transitive closure on weighted graphs, and can be computed efficiently using a modified Floyd-Warshall algorithm.  ...  We show that enforcing transitivity in affinity graphs leads to maximal transitive affinities which satisfy transitivity inequalities equivalent to ultra-metric and harmonic triangle inequalities.  ...  We prove that a modifed Floyd-Warshall algorithm is optimally efficient to compute transitive closures.  ... 
doi:10.1504/ijdmb.2006.010854 pmid:18399069 fatcat:cv35a7azvvgndog6cnnfnbx4gu

Context-Free Path Querying by Matrix Multiplication [article]

Rustam Azimov, Semyon Grigorev
2017 arXiv   pre-print
In this paper, we show how the context-free path query evaluation using these query semantics can be reduced to the calculation of the matrix transitive closure.  ...  Also, we propose an algorithm for context-free path query evaluation which uses relational query semantics and is based on matrix operations that make it possible to speed up computations by using a GPU  ...  ACKNOWLEDGMENTS We are grateful to Dmitri Boulytchev, Ekaterina Verbitskaia, Marina Polubelova, Dmitrii Kosarev and Dmitry Koznov for their careful reading, pointing out some mistakes, and invaluable suggestions  ... 
arXiv:1707.01007v2 fatcat:nvm4a7hzpjghdk5cjgc5kdpvtm

Accelerating Minimum Cost Polygon Triangulation Code with the TRACO Compiler

Marek Pałkowski, Wlodzimierz Bielecki
2018 Communication Papers of the 2018 Federated Conference on Computer Science and Information Systems  
First, the code is tiled by means of the transitive closure of a dependence graph. TRACO allows for tiling of the innermost loop nest that is not possible by means of other closely related compilers.  ...  An experimental study carried out on multi-core computers demonstrates considerable speed-up of tiled code, which overcomes that obtained for code generated with the closely related PLuTo compiler based  ...  CONCLUSION In this paper, we presented the usage of the TRACO compiler, implementing optimizing loop nest algorithms based on the transitive closure of dependence graphs, to the dynamic programming of  ... 
doi:10.15439/2018f8 dblp:conf/fedcsis/PalkowskiB18 fatcat:rjaa7gidubhvribnhvgir6nl3m

A mathematical model for integrated diagnostics

J.W. Sheppard, W.R. Simpson
1991 IEEE Design & Test of Computers  
Figure 1 .Figure 2 . 12 Dependency diagram for the case study First-order dependency matrices for the case study: Figure 3 .and 3 Algorithm for computing transitive closure. qFb,=' D,J = [ D . l~j )  ...  The first step in preprocessing is to compute the transitive closure of the dependencies in the model. Several algorithms exist for this computation."  ... 
doi:10.1109/54.107203 fatcat:qxbdbcr6ineovi5wkelp7b7ete

Automatic database normalization and primary key generation

Amir Hassan Bahmani, Mahmoud Naghibzadeh, Behnam Bahmani
2008 Canadian Conference on Electrical and Computer Engineering (CCECE)  
It produces the dependency matrix and the directed graph matrix, first. It then proceeds with generating the 2NF, 3NF, and BCNF normal forms. All tables are also generated as the procedure proceeds.  ...  Normalization is the most exercised technique for the analysis of relational databases.  ...  The process is based on the generation of dependency matrix, directed graph matrix, and determinant key transitive dependency matrix. The details of the methods for 2NF, 3NF, and BCNF are discussed.  ... 
doi:10.1109/ccece.2008.4564486 fatcat:wmivifzm65emhphb33f3xid4aa

Fast Algorithm for Calculating Transitive Closures of Binary Relations in the Structure of a Network Object

Vladimir Batsamut, Sviatoslav Manzura, Oleksandr Kosiak, Viacheslav Garmash, Dmytro Kukharets
2021 International Scientific Journal of Computing  
The corresponding graphs of the obtained dependences are given.  ...  The article proposes a fast algorithm for constructing the transitive closures between all pairs of nodes in the structure of a network object, which can have both directional and non-directional links  ...  The transitive closure matrix + G R of the original arbitrary graph G is calculated on the basis of the adjacency matrix G S in two rounds (m=2) of the current array by disjunctive embedding into the analyzed  ... 
doi:10.47839/ijc.20.4.2444 fatcat:23xfkdgpqvhczn3xnd4eucyili

Optimization of Linear Recursive Queries in SQL

Carlos Ordonez
2010 IEEE Transactions on Knowledge and Data Engineering  
Query optimization is studied with two important graph problems: computing the transitive closure of a graph and getting the power matrix of its adjacency matrix.  ...  We present SQL implementations for two fundamental algorithms: Seminaive and Direct.  ...  Duplicates can be efficiently eliminated exploiting an index on either (i, j) for the transitive closure of (d, i, j) for the power matrix.  ... 
doi:10.1109/tkde.2009.83 fatcat:qopingnlorfdhlnlygjrbcj6ly

Mantaining Dynamic Matrices for Fully Dynamic Transitive Closure [article]

Camil Demetrescu, Giuseppe F. Italiano
2001 arXiv   pre-print
Our matrix-based approach yields an algorithm for directed acyclic graphs that breaks through the O(n^2) barrier on the single-operation complexity of fully dynamic transitive closure.  ...  With this technique, we improve the best known bounds for fully dynamic transitive closure.  ...  Acknowledgements We are indebted to Garry Sagert and Mikkel Thorup for enlightening discussions, and to Valerie King for many useful comments and insights on this work.  ... 
arXiv:cs/0104001v1 fatcat:brp2hexcxfanvjhqzbh5kugarq

Dependencies Management in Dynamically Updateable Component-Based Systems

Saleh Alhazbi, Aman Jantan
2007 Journal of Computer Science  
It presents a service-based matrix model and nested graph as approaches to capture components' dependencies; it discusses using dependencies analysis for safe dynamic updating in component-based software  ...  This paper discusses dependencies analysis significance when updating component-based system dynamically.  ...  To compute the transitive closure, an adjacency matrix is required to capture such graph.  ... 
doi:10.3844/jcssp.2007.499.505 fatcat:rj2n7fxw65gwhktekcf7ymek4m
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