Encyclopedia of Big Data Technologies

Living Edition
| Editors: Sherif Sakr, Albert Zomaya

Graph Partitioning: Formulations and Applications to Big Data

  • Christian SchulzEmail author
  • Darren Strash
Living reference work entry

Latest version View entry history

First Online:
DOI: https://doi.org/10.1007/978-3-319-63962-8_312-2
How to cite

Definitions

Given an input graph G = (V, E) and an integer k ≥ 2, the graph partitioning problem is to divide V  into k disjoint blocks of vertices V1, V2, …, Vk, such that ∪1≤i≤kVi = V , while simultaneously optimizing an objective function and maintaining balance: \(|V_i|\leq (1+\epsilon )\left \lceil |V| / k\right \rceil \)

This is a preview of subscription content, log in to check access.

References

  1. Akhremtsev Y, Sanders P, Schulz C (2015) (Semi-)external algorithms for graph partitioning and clustering. In: Proceeding of 17th workshop on algorithm engineering and experiments (ALENEX 2015). SIAM, pp 33–43Google Scholar
  2. Alpert CJ, Kahng AB, Yao SZ (1999) Spectral partitioning with multiple eigenvectors. Discret Appl Math 90(1):3–26Google Scholar
  3. Andreev K, Räcke H (2006) Balanced graph partitioning. Theory Comput Syst 39(6):929–939Google Scholar
  4. Arz J, Sanders P, Stegmaier J, Mikut R (2017) 3D cell nuclei segmentation with balanced graph partitioning. CoRR abs/1702.05413Google Scholar
  5. Aydin K, Bateni M, Mirrokni V (2016) Distributed balanced partitioning via linear embedding. In: Proceeding of the ninth ACM international conference on web search and data mining. ACM, pp 387–396Google Scholar
  6. Bichot C, Siarry P (eds) (2011) Graph partitioning. Wiley, LondonGoogle Scholar
  7. Bourse F, Lelarge M, Vojnovic M (2014) Balanced graph edge partition. In: Proceeding 20th ACM SIGKDD international conference on knowledge discovery and data mining, KDD’14. ACM, pp 1456–1465Google Scholar
  8. Buluç A, Madduri K (2012) Graph partitioning for scalable distributed graph computations. In: Proceeding of 10th DIMACS implementation challenge, contemporary mathematics. AMS, pp 83–102Google Scholar
  9. Buluç A, Meyerhenke H, Safro I, Sanders P, Schulz C (2016) Recent advances in graph partitioning. In: Kliemann L, Sanders P (eds) Algorithm engineering. Springer, Cham, pp 117–158Google Scholar
  10. Fiduccia CM, Mattheyses RM (1982) A linear-time heuristic for improving network partitions. In: Proceedings of the 19th conference on design automation, pp 175–181Google Scholar
  11. Fietz J, Krause M, Schulz C, Sanders P, Heuveline V (2012) Optimized hybrid parallel lattice Boltzmann fluid flow simulations on complex geometries. In: Proceeding of Euro-Par 2012 parallel processing. LNCS, vol 7484. Springer, pp 818–829Google Scholar
  12. Gonzalez JE, Low Y, Gu H, Bickson D, Guestrin C (2012) PowerGraph: distributed graph-parallel computation on natural graphs. In: Presented as part of the 10th USENIX symposium on operating systems design and implementation (OSDI 12), USENIX, pp 17–30Google Scholar
  13. Hendrickson B, Kolda TG (2000) Graph partitioning models for parallel computing. Parallel Comput 26(12):1519–1534Google Scholar
  14. Hendrickson B, Leland R (1995) A multilevel algorithm for partitioning graphs. In: Proceeding of the ACM/IEEE conference on supercomputing’95. ACMGoogle Scholar
  15. Hyafil L, Rivest R (1973) Graph partitioning and constructing optimal decision trees are polynomial complete problems. Technical report 33, IRIA – Laboratoire de Recherche en Informatique et AutomatiqueGoogle Scholar
  16. Jammula N, Chockalingam SP, Aluru S (2017) Distributed memory partitioning of high-throughput sequencing datasets for enabling parallel genomics analyses. In: Proceeding of 8th ACM international conference on bioinformatics, computational biology, and health informatics, ACM-BCB’17. ACM, pp 417–424Google Scholar
  17. Karypis G, Aggarwal R, Kumar V, Shekhar S (1999) Multilevel hypergraph partitioning: applications in VLSI domain. IEEE Trans Very Large Scale Integr (VLSI) Syst 7(1):69–79Google Scholar
  18. Kim J, Hwang I, Kim YH, Moon BR (2011) Genetic approaches for graph partitioning: a survey. In: 13th genetic and evolutionary computation (GECCO). ACM, pp 473–480Google Scholar
  19. Lamm S, Sanders P, Schulz C, Strash D, Werneck RF (2017) Finding near-optimal independent sets at scale. J Heuristics 23(4):207–229Google Scholar
  20. Lang K, Rao S (2004) A flow-based method for improving the expansion or conductance of graph cuts. In: Proceedings of the 10th international integer programming and combinatorial optimization conference. LNCS, vol 3064. Springer, pp 383–400Google Scholar
  21. Langguth J, Sourouri M, Lines GT, Baden SB, Cai X (2015) Scalable heterogeneous CPU-GPU computations for unstructured tetrahedral meshes. IEEE Micro 35(4):6–15Google Scholar
  22. Li L, Geda R, Hayes AB, Chen Y, Chaudhari P, Zhang EZ, Szegedy M (2017) A simple yet effective balanced edge partition model for parallel computing. Proc ACM Meas Anal Comput Syst 1(1):14:1–14:21Google Scholar
  23. McCune RR, Weninger T, Madey G (2015) Thinking like a vertex: a survey of vertex-centric frameworks for large-scale distributed graph processing. ACM Comput Surv 48(2):25:1–25:39Google Scholar
  24. Meyerhenke H, Sauerwald T (2012) Beyond good partition shapes: an analysis of diffusive graph partitioning. Algorithmica 64(3):329–361Google Scholar
  25. Meyerhenke H, Sanders P, Schulz C (2017) Parallel graph partitioning for complex networks. IEEE Trans Parallel Distrib Syst 28:2625–2638Google Scholar
  26. Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76(3):036106Google Scholar
  27. Rahimian F, Payberah AH, Girdzijauskas S, Haridi S (2014) Distributed vertex-cut partitioning. In: IFIP international conference on distributed applications and interoperable systems. Springer, pp 186–200Google Scholar
  28. Sanders P, Schulz C (2011) Engineering multilevel graph partitioning algorithms. In: Proceedings of the 19th European symposium on algorithms. LNCS, vol 6942. Springer, pp 469–480Google Scholar
  29. Sanders P, Schulz C (2013) High quality graph partitioning. In: Proceedings of the 10th DIMACS implementation challenge – graph clustering and graph partitioning. AMS, pp 1–17Google Scholar
  30. Schloegel K, Karypis G, Kumar V (2003) Graph partitioning for high-performance scientific simulations. In: Dongarra J, Foster I, Fox G, Gropp W, Kennedy K, Torczon L, White A (eds) Sourcebook of parallel computing. Morgan Kaufmann Publishers, San Francisco, pp 491–541Google Scholar
  31. Shalita A, Karrer B, Kabiljo I, Sharma A, Presta A, Adcock A, Kllapi H, Stumm M (2016) Social hash: an assignment framework for optimizing distributed systems operations on social networks. In: Argyraki KJ, Isaacs R (eds) 13th USENIX symposium on networked systems design and implementation, NSDI. USENIX Association, pp 455–468Google Scholar
  32. Slota GM, Rajamanickam S, Devine K, Madduri K (2017) Partitioning trillion-edge graphs in minutes. In: Proceedings of the 31st IEEE international parallel and distributed processing symposium (IPDPS 2017), pp 646–655Google Scholar
  33. Tomer R, Khairy K, Amat F, Keller PJ (2012) Quantitative high-speed imaging of entire developing embryos with simultaneous multiview light-sheet microscopy. Nat Methods 9(7):755–763CrossRefGoogle Scholar
  34. Tran DA, Nguyen K, Pham C (2012) S-clone: socially-aware data replication for social networks. Comput Netw 56(7):2001–2013CrossRefGoogle Scholar
  35. Ugander J, Backstrom L (2013) Balanced label propagation for partitioning massive graphs. In: Proceedings of the sixth ACM international conference on web search and data mining, WSDM’13. ACM, pp 507–516Google Scholar
  36. Zhou M, Sahni O, Devine KD, Shephard MS, Jansen KE (2010) Controlling unstructured mesh partitions for massively parallel simulations. SIAM J Sci Comput 32(6):3201–3227MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of ViennaViennaAustria
  2. 2.Department of Computer ScienceColgate UniversityHamiltonUSA

Section editors and affiliations

  • Hannes Voigt
    • 1
  • George Fletcher
    • 2
  1. 1.Dresden Database Systems GroupTechnische Universität DresdenDresdenGermany
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of Technology