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Wlodzimierz Bielecki - One of the best experts on this subject based on the ideXlab platform.
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a practical approach to tiling zuker s rna folding using the Transitive Closure of loop dependence graphs
International Conference on Information Systems, 2017Co-Authors: Marek Palkowski, Wlodzimierz BieleckiAbstract:RNA secondary structure prediction is a computationally-intensive task that lies at the core of search applications in bioinformatics. In this paper, we consider Zuker’s RNA folding algorithm, which is challenging to optimize because it is resource intensive and has a large number of non-uniform dependences. We describe the application of a previously published approach, proposed by us, to automatic tiling Zuker’s RNA Folding loop nest using the exact polyhedral representation of dependences exposed for this nest. First, rectangular tiles are formed within the iteration space of Zuker’s loop nest. Then tiles are corrected to honor all dependences, exposed for the original loop nest, by means of applying the exact Transitive Closure of a dependence graph. We implemented our approach as a part of the source-to-source TRACO compiler. The experimental results present the significant speed-up factor of tiled code on a single core of a modern processor. Related work and future algorithm improvements are discussed.
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parallel tiled nussinov rna folding loop nest generated using both dependence graph Transitive Closure and loop skewing
BMC Bioinformatics, 2017Co-Authors: Marek Palkowski, Wlodzimierz BieleckiAbstract:RNA secondary structure prediction is a compute intensive task that lies at the core of several search algorithms in bioinformatics. Fortunately, the RNA folding approaches, such as the Nussinov base pair maximization, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. Polyhedral compilation techniques have proven to be a powerful tool for optimization of dense array codes. However, classical affine loop nest transformations used with these techniques do not optimize effectively codes of dynamic programming of RNA structure predictions. The purpose of this paper is to present a novel approach allowing for generation of a parallel tiled Nussinov RNA loop nest exposing significantly higher performance than that of known related code. This effect is achieved due to improving code locality and calculation parallelization. In order to improve code locality, we apply our previously published technique of automatic loop nest tiling to all the three loops of the Nussinov loop nest. This approach first forms original rectangular 3D tiles and then corrects them to establish their validity by means of applying the Transitive Closure of a dependence graph. To produce parallel code, we apply the loop skewing technique to a tiled Nussinov loop nest. The technique is implemented as a part of the publicly available polyhedral source-to-source TRACO compiler. Generated code was run on modern Intel multi-core processors and coprocessors. We present the speed-up factor of generated Nussinov RNA parallel code and demonstrate that it is considerably faster than related codes in which only the two outer loops of the Nussinov loop nest are tiled.
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Parallel tiled Nussinov RNA folding loop nest generated using both dependence graph Transitive Closure and loop skewing
BMC Bioinformatics, 2017Co-Authors: Marek Palkowski, Wlodzimierz BieleckiAbstract:Background RNA secondary structure prediction is a compute intensive task that lies at the core of several search algorithms in bioinformatics. Fortunately, the RNA folding approaches, such as the Nussinov base pair maximization, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. Polyhedral compilation techniques have proven to be a powerful tool for optimization of dense array codes. However, classical affine loop nest transformations used with these techniques do not optimize effectively codes of dynamic programming of RNA structure predictions. Results The purpose of this paper is to present a novel approach allowing for generation of a parallel tiled Nussinov RNA loop nest exposing significantly higher performance than that of known related code. This effect is achieved due to improving code locality and calculation parallelization. In order to improve code locality, we apply our previously published technique of automatic loop nest tiling to all the three loops of the Nussinov loop nest. This approach first forms original rectangular 3D tiles and then corrects them to establish their validity by means of applying the Transitive Closure of a dependence graph. To produce parallel code, we apply the loop skewing technique to a tiled Nussinov loop nest. Conclusions The technique is implemented as a part of the publicly available polyhedral source-to-source TRACO compiler. Generated code was run on modern Intel multi-core processors and coprocessors. We present the speed-up factor of generated Nussinov RNA parallel code and demonstrate that it is considerably faster than related codes in which only the two outer loops of the Nussinov loop nest are tiled.
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perfectly nested loop tiling transformations based on the Transitive Closure of the program dependence graph
Applied Categorical Structures, 2015Co-Authors: Wlodzimierz Bielecki, Marek PalkowskiAbstract:A novel approach to producing tiled code for perfectly nested loops is presented. It is based on the Transitive Closure of the program dependence graph. The approach is derived via a combination of the Polyhedral and Iteration Space Slicing frameworks that allows us to enlarge the effectiveness of the tiling transformation. The results of the evaluation of the effectiveness of a presented algorithm and the efficiency of tiled codes produced by means of the algorithm are discussed.
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calculating exact Transitive Closure for a normalized affine integer tuple relation
Electronic Notes in Discrete Mathematics, 2009Co-Authors: Wlodzimierz Bielecki, Tomasz Klimek, Konrad TrifunovicAbstract:Abstract An approach to calculate the exact Transitive Closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. The exact Transitive Closure calculation is based on resolving a system of recurrence equations being formed from the input and output tuples of a normalized relation. The approach permits for calculating an exact Transitive Closure for a relation when the constraints of this Closure are represented by both affine and non-linear forms. An example of calculating the exact Transitive Closure of normalized affine integer tuple relation is presented.
Marek Palkowski - One of the best experts on this subject based on the ideXlab platform.
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a practical approach to tiling zuker s rna folding using the Transitive Closure of loop dependence graphs
International Conference on Information Systems, 2017Co-Authors: Marek Palkowski, Wlodzimierz BieleckiAbstract:RNA secondary structure prediction is a computationally-intensive task that lies at the core of search applications in bioinformatics. In this paper, we consider Zuker’s RNA folding algorithm, which is challenging to optimize because it is resource intensive and has a large number of non-uniform dependences. We describe the application of a previously published approach, proposed by us, to automatic tiling Zuker’s RNA Folding loop nest using the exact polyhedral representation of dependences exposed for this nest. First, rectangular tiles are formed within the iteration space of Zuker’s loop nest. Then tiles are corrected to honor all dependences, exposed for the original loop nest, by means of applying the exact Transitive Closure of a dependence graph. We implemented our approach as a part of the source-to-source TRACO compiler. The experimental results present the significant speed-up factor of tiled code on a single core of a modern processor. Related work and future algorithm improvements are discussed.
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parallel tiled nussinov rna folding loop nest generated using both dependence graph Transitive Closure and loop skewing
BMC Bioinformatics, 2017Co-Authors: Marek Palkowski, Wlodzimierz BieleckiAbstract:RNA secondary structure prediction is a compute intensive task that lies at the core of several search algorithms in bioinformatics. Fortunately, the RNA folding approaches, such as the Nussinov base pair maximization, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. Polyhedral compilation techniques have proven to be a powerful tool for optimization of dense array codes. However, classical affine loop nest transformations used with these techniques do not optimize effectively codes of dynamic programming of RNA structure predictions. The purpose of this paper is to present a novel approach allowing for generation of a parallel tiled Nussinov RNA loop nest exposing significantly higher performance than that of known related code. This effect is achieved due to improving code locality and calculation parallelization. In order to improve code locality, we apply our previously published technique of automatic loop nest tiling to all the three loops of the Nussinov loop nest. This approach first forms original rectangular 3D tiles and then corrects them to establish their validity by means of applying the Transitive Closure of a dependence graph. To produce parallel code, we apply the loop skewing technique to a tiled Nussinov loop nest. The technique is implemented as a part of the publicly available polyhedral source-to-source TRACO compiler. Generated code was run on modern Intel multi-core processors and coprocessors. We present the speed-up factor of generated Nussinov RNA parallel code and demonstrate that it is considerably faster than related codes in which only the two outer loops of the Nussinov loop nest are tiled.
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Parallel tiled Nussinov RNA folding loop nest generated using both dependence graph Transitive Closure and loop skewing
BMC Bioinformatics, 2017Co-Authors: Marek Palkowski, Wlodzimierz BieleckiAbstract:Background RNA secondary structure prediction is a compute intensive task that lies at the core of several search algorithms in bioinformatics. Fortunately, the RNA folding approaches, such as the Nussinov base pair maximization, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. Polyhedral compilation techniques have proven to be a powerful tool for optimization of dense array codes. However, classical affine loop nest transformations used with these techniques do not optimize effectively codes of dynamic programming of RNA structure predictions. Results The purpose of this paper is to present a novel approach allowing for generation of a parallel tiled Nussinov RNA loop nest exposing significantly higher performance than that of known related code. This effect is achieved due to improving code locality and calculation parallelization. In order to improve code locality, we apply our previously published technique of automatic loop nest tiling to all the three loops of the Nussinov loop nest. This approach first forms original rectangular 3D tiles and then corrects them to establish their validity by means of applying the Transitive Closure of a dependence graph. To produce parallel code, we apply the loop skewing technique to a tiled Nussinov loop nest. Conclusions The technique is implemented as a part of the publicly available polyhedral source-to-source TRACO compiler. Generated code was run on modern Intel multi-core processors and coprocessors. We present the speed-up factor of generated Nussinov RNA parallel code and demonstrate that it is considerably faster than related codes in which only the two outer loops of the Nussinov loop nest are tiled.
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perfectly nested loop tiling transformations based on the Transitive Closure of the program dependence graph
Applied Categorical Structures, 2015Co-Authors: Wlodzimierz Bielecki, Marek PalkowskiAbstract:A novel approach to producing tiled code for perfectly nested loops is presented. It is based on the Transitive Closure of the program dependence graph. The approach is derived via a combination of the Polyhedral and Iteration Space Slicing frameworks that allows us to enlarge the effectiveness of the tiling transformation. The results of the evaluation of the effectiveness of a presented algorithm and the efficiency of tiled codes produced by means of the algorithm are discussed.
George H L Fletcher - One of the best experts on this subject based on the ideXlab platform.
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comparing the expressiveness of downward fragments of the relation algebra with Transitive Closure on trees
Information Systems, 2020Co-Authors: Jelle Hellings, Stijn Vansummeren, Marc Gyssens, Dirk Van Gucht, Jan Van Den Bussche, George H L FletcherAbstract:Abstract Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add Transitive Closure, projections, coprojections, intersection, and difference; this for Boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.
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Comparing Downward Fragments of the Relational Calculus with Transitive Closure on Trees
arXiv: Databases, 2018Co-Authors: Jelle Hellings, Stijn Vansummeren, Dirk Van Gucht, Jan Van Den Bussche, Marc Gyssens, Yuqing Wu, George H L FletcherAbstract:Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add Transitive Closure, projections, coprojections, intersection, and difference; this for boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.
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relative expressive power of navigational querying on graphs using Transitive Closure
Logic Journal of the IGPL, 2015Co-Authors: Dimitri Surinx, George H L Fletcher, Dirk Leinders, Stijn Vansummeren, Dirk Van Gucht, Jan Van Den Bussche, Marc Gyssens, Yuqing WuAbstract:Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of thefollowing operators: intersection; set difference; projection; coprojection; converse; Transitive Closure; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages, both for binary-relation queries as well as for boolean queries. In the absence of Transitive Closure, a complete Hasse diagram of relative expressiveness has already been established [8]. Moreover, it has already been shown that for boolean queries over a single edge label, Transitive Closure does not add any expressive power when only projection and diversity may be present [11]. In the present paper, we now complete the Hasse diagram in the presence of Transitive Closure, both for the case of a single edge label, as well as for the case of at least two edge labels. The main technical results are the following:1. In contrast to the above-stated result [11] Transitive Closure does add expressive power when coprojection is present.2. Transitive Closure also adds expressive power as soon as converse is present.3. Conversely, converse adds expressive power in the presence of Transitive Closure. In particular, the converse elimination result from [8] no longer works in the presence of Transitive Closure.4. As a corollary, we show that the converse elimination result from [8] necessitates an exponential blow-up in the degree of the expressions.
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the impact of Transitive Closure on the expressiveness of navigational query languages on unlabeled graphs
Annals of Mathematics and Artificial Intelligence, 2015Co-Authors: George H L Fletcher, Dirk Leinders, Marc Gyssens, Dirk Van Gucht, Jan Van Den Bussche, Stijn VansummerenAbstract:Several established and novel applications motivate us to study the expressive power of navigational query languages on graphs, which represent binary relations. Our basic language has only the operators union and composition, together with the identity relation. Richer languages can be obtained by adding other features such as intersection, difference, projection and coprojection, converse, and the diversity relation. The expressive power of the languages thus obtained cannot only be evaluated at the level of path queries (queries returning binary relations), but also at the level of Boolean or yes/no queries (expressed by the nonemptiness of an expression). For the languages considered above, adding Transitive Closure augments the expressive power not only at the level of path queries but also at the level of Boolean queries, for the latter provided that multiple input relations are allowed. This is no longer true in the context of unlabeled graphs (i.e., in the case where there is only one input relation), however. In this paper, we prove that this is indeed not the case for the basic language to which none, one, or both of projection and the diversity relation are added, a surprising result given the limited expressive power of these languages. In combination with earlier work (Fletcher et al. 2011, 2012), this result yields a complete understanding of the impact of Transitive Closure on the languages under consideration.
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the impact of Transitive Closure on the boolean expressiveness of navigational query languages on graphs
Foundations of Information and Knowledge Systems, 2012Co-Authors: George H L Fletcher, Dirk Leinders, Marc Gyssens, Dirk Van Gucht, Jan Van Den Bussche, Stijn VansummerenAbstract:Several established and novel applications motivate us to study the expressive power of navigational query languages on graphs, which represent binary relations. Our basic language has only the operators union and composition, together with the identity relation. Richer languages can be obtained by adding other features such as other set operators, projection and coprojection, converse, and the diversity relation. In this paper, we show that, when evaluated at the level of boolean queries with an unlabeled input graph (i.e., a single relation), adding Transitive Closure to the languages with coprojection adds expressive power, while this is not the case for the basic language to which none, one, or both of projection and the diversity relation are added. In combination with earlier work [10], these results yield a complete understanding of the impact of Transitive Closure on the languages under consideration.
Jelle Hellings - One of the best experts on this subject based on the ideXlab platform.
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comparing the expressiveness of downward fragments of the relation algebra with Transitive Closure on trees
Information Systems, 2020Co-Authors: Jelle Hellings, Stijn Vansummeren, Marc Gyssens, Dirk Van Gucht, Jan Van Den Bussche, George H L FletcherAbstract:Abstract Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add Transitive Closure, projections, coprojections, intersection, and difference; this for Boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.
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Comparing Downward Fragments of the Relational Calculus with Transitive Closure on Trees
arXiv: Databases, 2018Co-Authors: Jelle Hellings, Stijn Vansummeren, Dirk Van Gucht, Jan Van Den Bussche, Marc Gyssens, Yuqing Wu, George H L FletcherAbstract:Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add Transitive Closure, projections, coprojections, intersection, and difference; this for boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.
Marc Gyssens - One of the best experts on this subject based on the ideXlab platform.
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comparing the expressiveness of downward fragments of the relation algebra with Transitive Closure on trees
Information Systems, 2020Co-Authors: Jelle Hellings, Stijn Vansummeren, Marc Gyssens, Dirk Van Gucht, Jan Van Den Bussche, George H L FletcherAbstract:Abstract Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add Transitive Closure, projections, coprojections, intersection, and difference; this for Boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.
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Comparing Downward Fragments of the Relational Calculus with Transitive Closure on Trees
arXiv: Databases, 2018Co-Authors: Jelle Hellings, Stijn Vansummeren, Dirk Van Gucht, Jan Van Den Bussche, Marc Gyssens, Yuqing Wu, George H L FletcherAbstract:Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add Transitive Closure, projections, coprojections, intersection, and difference; this for boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.
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relative expressive power of navigational querying on graphs using Transitive Closure
Logic Journal of the IGPL, 2015Co-Authors: Dimitri Surinx, George H L Fletcher, Dirk Leinders, Stijn Vansummeren, Dirk Van Gucht, Jan Van Den Bussche, Marc Gyssens, Yuqing WuAbstract:Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of thefollowing operators: intersection; set difference; projection; coprojection; converse; Transitive Closure; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages, both for binary-relation queries as well as for boolean queries. In the absence of Transitive Closure, a complete Hasse diagram of relative expressiveness has already been established [8]. Moreover, it has already been shown that for boolean queries over a single edge label, Transitive Closure does not add any expressive power when only projection and diversity may be present [11]. In the present paper, we now complete the Hasse diagram in the presence of Transitive Closure, both for the case of a single edge label, as well as for the case of at least two edge labels. The main technical results are the following:1. In contrast to the above-stated result [11] Transitive Closure does add expressive power when coprojection is present.2. Transitive Closure also adds expressive power as soon as converse is present.3. Conversely, converse adds expressive power in the presence of Transitive Closure. In particular, the converse elimination result from [8] no longer works in the presence of Transitive Closure.4. As a corollary, we show that the converse elimination result from [8] necessitates an exponential blow-up in the degree of the expressions.
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the impact of Transitive Closure on the expressiveness of navigational query languages on unlabeled graphs
Annals of Mathematics and Artificial Intelligence, 2015Co-Authors: George H L Fletcher, Dirk Leinders, Marc Gyssens, Dirk Van Gucht, Jan Van Den Bussche, Stijn VansummerenAbstract:Several established and novel applications motivate us to study the expressive power of navigational query languages on graphs, which represent binary relations. Our basic language has only the operators union and composition, together with the identity relation. Richer languages can be obtained by adding other features such as intersection, difference, projection and coprojection, converse, and the diversity relation. The expressive power of the languages thus obtained cannot only be evaluated at the level of path queries (queries returning binary relations), but also at the level of Boolean or yes/no queries (expressed by the nonemptiness of an expression). For the languages considered above, adding Transitive Closure augments the expressive power not only at the level of path queries but also at the level of Boolean queries, for the latter provided that multiple input relations are allowed. This is no longer true in the context of unlabeled graphs (i.e., in the case where there is only one input relation), however. In this paper, we prove that this is indeed not the case for the basic language to which none, one, or both of projection and the diversity relation are added, a surprising result given the limited expressive power of these languages. In combination with earlier work (Fletcher et al. 2011, 2012), this result yields a complete understanding of the impact of Transitive Closure on the languages under consideration.
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the impact of Transitive Closure on the boolean expressiveness of navigational query languages on graphs
Foundations of Information and Knowledge Systems, 2012Co-Authors: George H L Fletcher, Dirk Leinders, Marc Gyssens, Dirk Van Gucht, Jan Van Den Bussche, Stijn VansummerenAbstract:Several established and novel applications motivate us to study the expressive power of navigational query languages on graphs, which represent binary relations. Our basic language has only the operators union and composition, together with the identity relation. Richer languages can be obtained by adding other features such as other set operators, projection and coprojection, converse, and the diversity relation. In this paper, we show that, when evaluated at the level of boolean queries with an unlabeled input graph (i.e., a single relation), adding Transitive Closure to the languages with coprojection adds expressive power, while this is not the case for the basic language to which none, one, or both of projection and the diversity relation are added. In combination with earlier work [10], these results yield a complete understanding of the impact of Transitive Closure on the languages under consideration.
