Evolutionary multi-level acyclic graph partitioning

Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing execution on multiprocessor architectures under hardware resource constraints. However due to progra...

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Vydané v:	Journal of heuristics Ročník 26; číslo 5; s. 771 - 799
Hlavní autori:	Moreira, Orlando, Popp, Merten, Schulz, Christian
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.10.2020 Springer Nature B.V
Predmet:	Artificial Intelligence Calculus of Variations and Optimal Control; Optimization Compilers Constraints Embedded systems Evolutionary algorithms Genetic algorithms Graph theory Graphs Hardware Heuristic Management Science Mathematics Mathematics and Statistics Multiprocessing Operations Research Operations Research/Decision Theory Parallel processing Partitioning Reduction Graph partitioning Computer vision Embedded systems Evolutionary algorithm Imaging
ISSN:	1381-1231, 1572-9397
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Abstract	Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing execution on multiprocessor architectures under hardware resource constraints. However due to program memory restrictions in embedded multiprocessor systems, applications need to be divided into parts without cyclic dependencies. We found that this can be done by a subsequent second graph partitioning step with an additional acyclicity constraint. We have four main contributions. First, we show that this more constrained version of the graph partitioning problem is NP-complete and present linear time heuristics. We then integrate them into an existing multi-level graph partitioning framework to better handle large graphs. This achieves a 9% reduction of the edge cut compared to the previous single-level algorithm. Based on this, we engineer an evolutionary algorithm to further reduce the cut, achieving a 30% reduction on average compared to the state of the art. Finally, we integrate the partitioning heuristics into a graph compiler for an embedded multiprocessor architecture and show that this can reduce the amount of communication for a real-world imaging application and thereby accelerate it by an average of 11%. It is shown that the compiler can emit optimized code for vastly different hardware platforms using the heuristics. In addition, we demonstrate how a custom fitness function for the evolutionary algorithm can be used to optimize other objectives like load balancing if the communication volume is not predominantly important on a given hardware platform.
AbstractList	Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing execution on multiprocessor architectures under hardware resource constraints. However due to program memory restrictions in embedded multiprocessor systems, applications need to be divided into parts without cyclic dependencies. We found that this can be done by a subsequent second graph partitioning step with an additional acyclicity constraint. We have four main contributions. First, we show that this more constrained version of the graph partitioning problem is NP-complete and present linear time heuristics. We then integrate them into an existing multi-level graph partitioning framework to better handle large graphs. This achieves a 9% reduction of the edge cut compared to the previous single-level algorithm. Based on this, we engineer an evolutionary algorithm to further reduce the cut, achieving a 30% reduction on average compared to the state of the art. Finally, we integrate the partitioning heuristics into a graph compiler for an embedded multiprocessor architecture and show that this can reduce the amount of communication for a real-world imaging application and thereby accelerate it by an average of 11%. It is shown that the compiler can emit optimized code for vastly different hardware platforms using the heuristics. In addition, we demonstrate how a custom fitness function for the evolutionary algorithm can be used to optimize other objectives like load balancing if the communication volume is not predominantly important on a given hardware platform. Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing execution on multiprocessor architectures under hardware resource constraints. However due to program memory restrictions in embedded multiprocessor systems, applications need to be divided into parts without cyclic dependencies. We found that this can be done by a subsequent second graph partitioning step with an additional acyclicity constraint. We have four main contributions. First, we show that this more constrained version of the graph partitioning problem is NP-complete and present linear time heuristics. We then integrate them into an existing multi-level graph partitioning framework to better handle large graphs. This achieves a 9% reduction of the edge cut compared to the previous single-level algorithm. Based on this, we engineer an evolutionary algorithm to further reduce the cut, achieving a 30% reduction on average compared to the state of the art. Finally, we integrate the partitioning heuristics into a graph compiler for an embedded multiprocessor architecture and show that this can reduce the amount of communication for a real-world imaging application and thereby accelerate it by an average of 11%. It is shown that the compiler can emit optimized code for vastly different hardware platforms using the heuristics. In addition, we demonstrate how a custom fitness function for the evolutionary algorithm can be used to optimize other objectives like load balancing if the communication volume is not predominantly important on a given hardware platform.
Author	Popp, Merten Schulz, Christian Moreira, Orlando
Author_xml	– sequence: 1 givenname: Orlando surname: Moreira fullname: Moreira, Orlando organization: GrAI Matter Labs – sequence: 2 givenname: Merten orcidid: 0000-0001-5916-8180 surname: Popp fullname: Popp, Merten email: mail@merten-popp.de organization: Braunschweig Institute of Technology – sequence: 3 givenname: Christian surname: Schulz fullname: Schulz, Christian organization: University of Vienna
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Cites_doi	10.1007/978-3-642-23719-5_40 10.1007/978-1-4614-6170-8_23 10.1145/368996.369025 10.1145/2001576.2001642 10.1109/CCGRID.2017.101 10.1162/evco.1996.4.2.113 10.1007/BFb0120902 10.1007/s00224-006-1350-7 10.1016/0743-7315(92)90014-E 10.1109/TPDS.2014.2312924 10.1145/2010324.1964963 10.1109/IPDPS.2006.1639360 10.1137/S1064827598337373 10.1007/978-3-319-07959-2_30 10.1109/IPDPS.2006.1639295 10.5220/0006223101440151 10.1007/978-94-017-7358-4_40-1 10.1137/S1064827595287997 10.4203/csets.17.2 10.1201/b11644-15 10.1007/978-1-4614-7705-1_1 10.1007/978-0-387-35498-9_43 10.1093/oso/9780195099713.001.0001 10.1007/978-3-642-22012-8_40 10.1109/TVLSI.2007.909806 10.1016/j.parco.2007.12.001 10.1098/rspa.1935.0134 10.1109/DAC.1982.1585498
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References_xml	– reference: Doerr, B., Fouz, M.: Asymptotically optimal randomized rumor spreading. In: Proceedings of the 38th International Colloquium on Automata, Languages and Programming, Proceedings, Part II, LNCS, vol. 6756, pp. 502–513. Springer (2011) – reference: Walshaw, C., Cross, M.: JOSTLE: parallel multilevel graph-partitioning software—an overview. In: Mesh Partitioning Techniques and Domain Decomposition Techniques, pp. 27–58 (2007) – reference: Abou-Rjeili, A., Karypis, G.: Multilevel algorithms for partitioning power-law graphs. In: Proceedings of 20th International Parallel and Distributed Processing Symposium (2006) – reference: KaoCCPerformance-oriented partitioning for task scheduling of parallel reconfigurable architecturesIEEE Trans. Parallel Distrib. Syst.201526385886710.1109/TPDS.2014.2312924 – reference: Meyerhenke, H., Sanders, P., Schulz, C.: Partitioning complex networks via size-constrained clustering. In: Proceedings of the 13th International Symposium on Experimental Algorithms, LNCS. Springer (2014) – reference: JiangYCWangJFTemporal partitioning data flow graphs for dynamically reconfigurable computingIEEE Trans. Very Large Scale Integr. VLSI Syst.200715121351136110.1109/TVLSI.2007.909806 – reference: Cardoso, J.M.P., Neto, H.C.: An enhanced static-list scheduling algorithm for temporal partitioning onto RPUs. In: VLSI: Systems on a Chip, pp. 485–496. Springer (2000) – reference: Pellegrini, F.: Scotch and PT-scotch graph partitioning software: an overview. In: Combinatorial Scientific Computing, pp. 373–406 (2012) – reference: Khronos Group: The OpenVX specification: vision functions. https://www.khronos.org/registry/OpenVX/specs/1.0/html/da/db6/group__group__vision__functions.html (2017) – reference: Bader, D.A., Meyerhenke, H., Sanders, P., Schulz, C., Kappes, A., Wagner, D.: Benchmarking for graph clustering and partitioning. In: Encyclopedia of Social Network Analysis and Mining (2014) – reference: BichotCSiarryPGraph Partitioning2011HobokenWiley1254.05148 – reference: PicardJCQueyranneMOn the structure of all minimum cuts in a network and applicationsMath. Program. Stud.19801381659208110.1007/BFb0120902 – reference: Herrmann, J., Kho, J., Uçar, B., Kaya, K., Çatalyürek, Ü.V.: Acyclic partitioning of large directed acyclic graphs. In: Proceedings of the 17th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing, pp. 371–380. IEEE Press (2017) – reference: AndreevKRäckeHBalanced graph partitioningTheory Comput. Syst.2006396929939227908210.1007/s00224-006-1350-7 – reference: Gary, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness (1979) – reference: ParisSHasinoffSWKautzJLocal Laplacian filters: edge-aware image processing with a Laplacian pyramidACM Trans. Graph.20113046810.1145/2010324.1964963 – reference: Wolf, M.: Embedded computer vision. 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Snippet	Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning...
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SubjectTerms	Artificial Intelligence Calculus of Variations and Optimal Control; Optimization Compilers Constraints Embedded systems Evolutionary algorithms Genetic algorithms Graph theory Graphs Hardware Heuristic Management Science Mathematics Mathematics and Statistics Multiprocessing Operations Research Operations Research/Decision Theory Parallel processing Partitioning Reduction
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Title	Evolutionary multi-level acyclic graph partitioning
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