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Graph Partitioning: Formulations and Applications to Big Data

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Encyclopedia of Big Data Technologies

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: \(|V_i|\leq (1+\epsilon )\left \lceil |V| / k\right \rceil \) for some 𝜖 ≥ 0.

Overview

Subdividing a problem into manageable pieces is a critical task in effectively parallelizing computation and even accelerating sequential computation. A key method that has received a lot of attention for doing so is graph partitioning. The simplest and most common form of graph partitioning asks for the vertex set to be partitioned into k roughly equal-sized blocks while minimizing the number of edges between the blocks (called cut edges). Even this most basic variant is NP-hard (Hyafil and Rivest 1973). Graph partitioning has many application areas, including VLSI (Karypis et al. 1999), scientific computing (Langguth et al. 2015),...

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References

  • 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 33–43

    Google Scholar 

  • Alpert CJ, Kahng AB, Yao SZ (1999) Spectral partitioning with multiple eigenvectors. Discret Appl Math 90(1):3–26

    Article  MathSciNet  MATH  Google Scholar 

  • Andreev K, Räcke H (2006) Balanced graph partitioning. Theory Comput Syst 39(6):929–939

    Article  MathSciNet  MATH  Google Scholar 

  • Arz J, Sanders P, Stegmaier J, Mikut R (2017) 3D cell nuclei segmentation with balanced graph partitioning. CoRR abs/1702.05413

    Google Scholar 

  • 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 387–396

    Google Scholar 

  • Bichot C, Siarry P (eds) (2011) Graph partitioning. Wiley, London

    MATH  Google Scholar 

  • 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 1456–1465

    Google Scholar 

  • Buluç A, Madduri K (2012) Graph partitioning for scalable distributed graph computations. In: Proceeding of 10th DIMACS implementation challenge, contemporary mathematics. AMS, pp 83–102

    Google Scholar 

  • 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 117–158

    Chapter  Google Scholar 

  • Fiduccia CM, Mattheyses RM (1982) A linear-time heuristic for improving network partitions. In: Proceedings of the 19th conference on design automation, pp 175–181

    Google Scholar 

  • 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 818–829

    Google Scholar 

  • 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 17–30

    Google Scholar 

  • Hendrickson B, Kolda TG (2000) Graph partitioning models for parallel computing. Parallel Comput 26(12):1519–1534

    Article  MathSciNet  MATH  Google Scholar 

  • Hendrickson B, Leland R (1995) A multilevel algorithm for partitioning graphs. In: Proceeding of the ACM/IEEE conference on supercomputing’95. ACM

    Google Scholar 

  • 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 Automatique

    Google Scholar 

  • 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 417–424

    Google Scholar 

  • 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):69–79

    Article  Google Scholar 

  • 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 473–480

    Google Scholar 

  • Lamm S, Sanders P, Schulz C, Strash D, Werneck RF (2017) Finding near-optimal independent sets at scale. J Heuristics 23(4):207–229

    Article  MATH  Google Scholar 

  • 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 383–400

    Google Scholar 

  • Langguth J, Sourouri M, Lines GT, Baden SB, Cai X (2015) Scalable heterogeneous CPU-GPU computations for unstructured tetrahedral meshes. IEEE Micro 35(4):6–15

    Article  Google Scholar 

  • 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):14:1–14:21

    Article  Google Scholar 

  • 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):25:1–25:39

    Article  Google Scholar 

  • Meyerhenke H, Sauerwald T (2012) Beyond good partition shapes: an analysis of diffusive graph partitioning. Algorithmica 64(3):329–361

    Article  MathSciNet  MATH  Google Scholar 

  • Meyerhenke H, Sanders P, Schulz C (2017) Parallel graph partitioning for complex networks. IEEE Trans Parallel Distrib Syst 28:2625–2638

    Article  Google Scholar 

  • Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76(3):036106

    Article  Google Scholar 

  • 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 186–200

    Google Scholar 

  • Sanders P, Schulz C (2011) Engineering multilevel graph partitioning algorithms. In: Proceedings of the 19th European symposium on algorithms. LNCS, vol 6942. Springer, pp 469–480

    Google Scholar 

  • Sanders P, Schulz C (2013) High quality graph partitioning. In: Proceedings of the 10th DIMACS implementation challenge – graph clustering and graph partitioning. AMS, pp 1–17

    Google Scholar 

  • 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 491–541

    Google Scholar 

  • 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 455–468

    Google Scholar 

  • 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 646–655

    Google Scholar 

  • 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):755–763

    Article  Google Scholar 

  • Tran DA, Nguyen K, Pham C (2012) S-clone: socially-aware data replication for social networks. Comput Netw 56(7):2001–2013

    Article  Google Scholar 

  • 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 507–516

    Google Scholar 

  • 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):3201–3227

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Vienna, Vienna, Austria

    Christian Schulz

  2. Department of Computer Science, Colgate University, Hamilton, NY, USA

    Darren Strash

Authors
  1. Christian Schulz
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  2. Darren Strash
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Correspondence to Christian Schulz .

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Editors and Affiliations

  1. Institute of Computer Science, University of Tartu, Tartu, Estonia

    Sherif Sakr

  2. School of Information Technologies, Sydney University, Sydney, Australia

    Albert Y. Zomaya

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Schulz, C., Strash, D. (2019). Graph Partitioning: Formulations and Applications to Big Data. In: Sakr, S., Zomaya, A.Y. (eds) Encyclopedia of Big Data Technologies. Springer, Cham. https://doi.org/10.1007/978-3-319-77525-8_312

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