ABSTRACT
Computing high quality node separators in large graphs is necessary for a variety of applications, ranging from divide-and-conquer algorithms to VLSI design. In this work, we present a novel distributed evolutionary algorithm tackling the k-way node separator problem. A key component of our contribution includes new k-way local search algorithms based on maximum flows. We combine our local search with a multilevel approach to compute an initial population for our evolutionary algorithm, and further show how to modify the coarsening stage of our multilevel algorithm to create effective combine and mutation operations. Lastly, we combine these techniques with a scalable communication protocol, producing a system that is able to compute high quality solutions in a short amount of time. Our experiments against competing algorithms show that our advanced evolutionary algorithm computes the best result on 94% of the chosen benchmark instances.
- S. N. Bhatt and F. T. Leighton. 1984. A framework for solving VLSI graph layout problems. J. Comput. System Sci. 28, 2 (1984), 300 -- 343.Google ScholarCross Ref
- C. Bichot and P. Siarry (Eds.). 2011. Graph Partitioning. Wiley.Google Scholar
- T. N. Bui and C. Jones. 1992. Finding Good Approximate Vertex and Edge Partitions is NP-hard. Inform. Process. Lett. 42, 3 (1992), 153--159. Google ScholarDigital Library
- A. Buluç, H. Meyerhenke, I. Safro, P. Sanders, and C. Schulz. 2016. Recent Advances in Graph Partitioning. In Algorithm Engineering - Selected Results (LNCS), Vol. 9920. Springer, 117--158.Google Scholar
- T. Davis. 2017. The University of Florida Sparse Matrix Collection. (2017).Google Scholar
- D. Delling, M. Holzer, K. Müller, F. Schulz, and D. Wagner. 2009. High-performance multi-level routing. The Shortest Path Problem: Ninth DIMACS Implementation Challenge 74 (2009), 73--92.Google ScholarCross Ref
- J. Dibbelt, B. Strasser, and D. Wagner. 2014. Customizable contraction hierarchies. In 13th Int. Symp. on Exp. Algorithms (SEA'14). Springer, 271--282. Google ScholarDigital Library
- G. N. Federickson. 1987. Fast Algorithms for Shortest Paths in Planar Graphs, with Applications. SIAM J. Comput. 16, 6 (1987), 1004--1022. Google ScholarDigital Library
- J. Fukuyama. 2006. NP-Completeness of the Planar Separator Problems. Journal of Graph Algorithms and Applications 10, 2 (2006), 317--328.Google ScholarCross Ref
- M. R. Garey and D. S. Johnson. 2002. Computers and Intractability. Vol. 29. WH Freeman & Co., San Francisco.Google Scholar
- A. George. 1973. Nested Dissection of a Regular Finite Element Mesh. SIAM J. Numer. Anal. 10, 2 (1973), 345--363.Google ScholarDigital Library
- W. W. Hager, J. T. Hungerford, and I. Safro. 2014. A Multilevel Bilinear Programming Algorithm For the Vertex Separator Problem. Technical Report.Google Scholar
- M. Hamann and B. Strasser. 2016. Graph Bisection with Pareto-Optimization. In Proc. of the 18th Algorithm Engineering and Experiments. SIAM, 90--102.Google Scholar
- G. Karypis and V. Kumar. 1998. A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. SIAM J. on SC 20, 1 (1998), 359--392. Google ScholarDigital Library
- D. LaSalle and G. Karypis. 2015. Efficient Nested Dissection for Multicore Architectures. In Euro-Par 2015: Parallel Processing. Springer, 467--478.Google Scholar
- C. E. Leiserson. 1980. Area-Efficient Graph Layouts. In 21st Symp. on Foundations of Computer Science. IEEE, 270--281. Google ScholarDigital Library
- R. J. Lipton and R. E. Tarjan. 1979. A Separator Theorem for Planar Graphs. SIAM J. Appl. Math. 36, 2 (1979), 177--189.Google ScholarDigital Library
- R. J. Lipton and R. E. Tarjan. 1980. Applications of a Planar Separator Theorem. SIAM Journal On Computing 9, 3 (1980), 615--627.Google ScholarDigital Library
- J. Maue and P. Sanders. 2007. Engineering Algorithms for Approximate Weighted Matching. In Proceedings of the 6th Workshop on Experimental Algorithms (WEA'07) (LNCS), Vol. 4525. Springer, 242--255. Google ScholarDigital Library
- B. L Miller and D. E Goldberg. 1996. Genetic Algorithms, Tournament Selection, and the Effects of Noise. Evolutionary Computation 4, 2 (1996), 113--131. Google ScholarDigital Library
- F. Pellegrini. 2017. Scotch Home Page. (2017).Google Scholar
- D. C. Porumbel, J.-K. Hao, and P. Kuntz. 2011. Spacing memetic algorithms. In 13th Annual Genetic and Evolutionary Computation Conference, GECCO 2011, Proceedings, Dublin, Ireland, July 12--16, 2011. 1061--1068. Google ScholarDigital Library
- A. Pothen, H. D. Simon, and K. P. Liou. 1990. Partitioning Sparse Matrices with Eigenvectors of Graphs. SIAM J. Matrix Anal. Appl. 11, 3 (1990), 430--452. Google ScholarDigital Library
- P. Sanders and C. Schulz. 2012. Distributed Evolutionary Graph Partitioning. In Proc. of the 12th Workshop on Algorithm Engineering and Experimentation (ALENEX'12). 16--29. Google ScholarDigital Library
- P. Sanders and C. Schulz. 2013. KaHIP - Karlsruhe High Qualtity Partitioning Homepage. (2013). http://algo2.iti.kit.edu/documents/kahip/index.html.Google Scholar
- P. Sanders and C. Schulz. 2016. Advanced Multilevel Node Separator Algorithms. In 15th Int. Sym. on Exp. Algorithms, SEA 2016, Vol. 9685. Springer, 294--309. Google ScholarDigital Library
- A. J. Soper, C. Walshaw, and M. Cross. 2004. A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning. Journal of Global Optimization 29, 2 (2004), 225--241. Google ScholarDigital Library
- R. Williger. 2016. Evolutionary k-way Node Separators. Bachelor's Thesis. Karlsruhe Institute of Technologie.Google Scholar
Index Terms
- Distributed evolutionary k-way node separators
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