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Graph Partitioning with Acyclicity Constraints

Authors Orlando Moreira, Merten Popp, Christian Schulz

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  • Graph Partitioning
  • Computer Vision and Imaging Applications

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Abstract

Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in multiprocessor scheduling. We identified the additional constraint of acyclic dependencies between blocks when mapping streaming applications to a heterogeneous embedded multiprocessor. Existing algorithms and heuristics do not address this requirement and deliver results that are not applicable for our use-case. In this work, we show that this more constrained version of the graph partitioning problem is NP-complete and present heuristics that achieve a close approximation of the optimal solution found by an exhaustive search for small problem instances and much better scalability for larger instances. In addition, we can show a positive impact on the schedule of a real imaging application that improves communication volume and execution time.

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Orlando Moreira, Merten Popp, and Christian Schulz. Graph Partitioning with Acyclicity Constraints. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.SEA.2017.30

Author Details

Orlando Moreira
Merten Popp
Christian Schulz

References

  1. A. Abou-Rjeili and G. Karypis. Multilevel Algorithms for Partitioning Power-Law Graphs. In Proc. of 20th IPDPS, 2006. Google Scholar
  2. K. Andreev and H. Räcke. Balanced Graph Partitioning. Theory of Computing Systems, 39(6):929-939, 2006. Google Scholar
  3. D. A. Bader, H. Meyerhenke, P. Sanders, C. Schulz, A. Kappes, and D. Wagner. Benchmarking for Graph Clustering and Partitioning. In Encyclopedia of Social Network Analysis and Mining, to appear. Google Scholar
  4. C. Bichot and P. Siarry, editors. Graph Partitioning. Wiley, 2011. Google Scholar
  5. A. Buluç, H. Meyerhenke, I. Safro, P. Sanders, and C. Schulz. Recent Advances in Graph Partitioning. In Algorithm Engineering - Selected Topics, to app., ArXiv:1311.3144, 2014. Google Scholar
  6. C. Chevalier and F. Pellegrini. PT-Scotch. Parallel Computing, 34(6-8):318-331, 2008. URL: http://dx.doi.org/10.1016/j.parco.2007.12.001.
  7. D. G. Feitelson and L. Rudolph. Gang scheduling performance benefits for fine-grain synchronization. Journal of Parallel and distributed Computing, 16(4):306-318, 1992. Google Scholar
  8. C. M. Fiduccia and R. M. Mattheyses. A Linear-Time Heuristic for Improving Network Partitions. In Proceedings of the 19th Conference on Design Automation, pages 175-181, 1982. Google Scholar
  9. M. R. Gary and D. S. Johnson. Computers and intractability: A guide to the theory of np-completeness, 1979. Google Scholar
  10. J. Goossens and P. Richard. Optimal scheduling of periodic gang tasks. Leibniz transactions on embedded systems, 3(1):04-1, 2016. Google Scholar
  11. Khronos Group. The OpenVX API. URL: https://www.khronos.org/openvx/.
  12. Khronos Group. The OpenVX Specification: Vision Functions. URL: https://www.khronos.org/registry/OpenVX/specs/1.0/html/da/db6/group__group__vision__functions.html.
  13. A. B. Kahn. Topological sorting of large networks. Communications of the ACM, 5(11):558-562, 1962. Google Scholar
  14. G. Karypis and V. Kumar. A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. SIAM Journal on Scientific Computing, 20(1):359-392, 1998. Google Scholar
  15. E. A. Lee and D. G. Messerschmitt. Synchronous data flow. Proceedings of the IEEE, 75(9):1235-1245, 1987. Google Scholar
  16. H. Meyerhenke, B. Monien, and S. Schamberger. Accelerating Shape Optimizing Load Balancing for Parallel FEM Simulations by Algebraic Multigrid. In Proc. of 20th IPDPS, 2006. Google Scholar
  17. P. R. Panda, F. Catthoor, N. D. Dutt, K. Danckaert, E. Brockmeyer, C. Kulkarni, A. Vandercappelle, and P. G. Kjeldsberg. Data and memory optimization techniques for embedded systems. ACM Transactions on Design Automation of Electronic Systems (TODAES), 6(2):149-206, 2001. Google Scholar
  18. S. Paris, S. W. Hasinoff, and J. Kautz. Local laplacian filters: edge-aware image processing with a laplacian pyramid. ACM Trans. Graph., 30(4):68, 2011. Google Scholar
  19. F. Pellegrini. Scotch Home Page. https://www.labri.fr/perso/pelegrin/scotch/.
  20. J. C. Picard and M. Queyranne. On the Structure of All Minimum Cuts in a Network and Applications. Mathematical Programming Studies, 13:8-16, 1980. Google Scholar
  21. E. Rainey, J. Villarreal, G. Dedeoglu, K. Pulli, T. Lepley, and F. Brill. Addressing system-level optimization with openvx graphs. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 644-649, 2014. Google Scholar
  22. P. Sanders and C. Schulz. Engineering Multilevel Graph Partitioning Algorithms. In Proc. of the 19th European Symp. on Algorithms, volume 6942 of LNCS, pages 469-480. Springer, 2011. Google Scholar
  23. K. Schloegel, G. Karypis, and V. Kumar. Graph Partitioning for High Performance Scientific Simulations. In The Sourcebook of Parallel Computing, pages 491-541, 2003. Google Scholar
  24. R. V. Southwell. Stress-Calculation in Frameworks by the Method of "Systematic Relaxation of Constraints". Proc. of the Royal Society of London, 151(872):56-95, 1935. Google Scholar
  25. G. L. Stavrinides and H. D. Karatza. Scheduling different types of applications in a saas cloud. In Proceedings of the 6th International Symposium on Business Modeling and Software Design (BMSD’16), pages 144-151, 2016. Google Scholar
  26. C. Walshaw and M. Cross. Mesh Partitioning: A Multilevel Balancing and Refinement Algorithm. SIAM Journal on Scientific Computing, 22(1):63-80, 2000. Google Scholar
  27. C. Walshaw and M. Cross. JOSTLE: Parallel Multilevel Graph-Partitioning Software - An Overview. In Mesh Partitioning Techniques and Domain Decomposition Techniques, pages 27-58. American Mathematical Society, 2007. Google Scholar
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