Skip to main content
SpringerLink
Log in

Lock-Gain Based Graph Partitioning

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

We propose a new heuristic for the graph partitioning problem. Based on the traditional iterative improvement framework, the heuristic uses a new type of gain in selecting vertices to move between partitions. The new type of gain provides a good explanation for the performance difference of tie-breaking strategies in KL-based iterative improvement graph partitioning algorithms. The new heuristic performed excellently. Theoretical arguments supporting its efficacy are also provided. As the proposed heuristic is considered a good candidate for local optimization engines in metaheuristics, we combined it with a genetic algorithm as a sample case and obtained a surprising result that even the average results over 1,000 runs equalled the best known for most graphs.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alpert, C.J. and A.B. Kahng. (1995). “Recent Directions in Netlist Partitioning: A Survey.” Integration: the VLSI Journal 19(1-2), 1–81.

    Google Scholar 

  • Battiti, R. and A. Bertossi. (1999). “Greedy, Prohibition, and Reactive Heuristics for Graph Partitioning.” IEEE Trans. on Computers 48(4), 361–385.

    Google Scholar 

  • Billings, D., N. Burch, A.Davidson, R. Holte, J. Schaeffer, T. Schauenberg, and D. Szafron. (2003). “Approximating Game-Theoretic Optimal Strategies for Full-Scale Poker.” In International Joint Conference on Artificial Intelligence, pp. 661-668.

  • Bui, T.N., S. Chaudhuri, F.T. Leighton, and M. Sipser. (1987). “Graph Bisection Algorithms with Good Average Case Behavior.” Combinatorica 7(2), 171–191.

    Google Scholar 

  • Bui, T.N. and C. Jones. (1992). “Finding Good Approximate Vertex and Edge Partitions is NP-Hard.” Information Processing Letters 42, 153–159.

    Google Scholar 

  • Bui, T.N. and B.R. Moon. (1996). “Genetic Algorithm and Graph Partitioning.” IEEE Trans. on Computers 45(7), 841–855.

    Google Scholar 

  • Chatterjee, A.C. and R. Hartley. (1990). “A New Simultaneous Circuit Partitioning Chip Placement Approach Based on Simulated Annealing.” In 27th ACM/IEEE Design Automation Conference, pp. 36-39.

  • Cohoon, J.P., W.N. Martin, and D.S. Richards. (1991). “A Multi-Population Genetic Algorithm for Solving the k-Partition Problem on Hyper-Cubes.” In Fourth International Conference on Genetic Algorithms, pp. 244-248.

  • Collins, R. and D. Jefferson. (1991). “Selection in Massively Parallel Genetic Algorithms.” In Fourth International Conference on Genetic Algorithms, pp. 249-256.

  • Dell'Amico, M. and F. Maffioli. (1996). “A New Tabu Search Approach to the 0-1 Equicut Problem.” In Meta-Heuristics 1995: The State of the Art, Kluwer Academic, pp. 361-377.

  • Dutt, S. and W. Deng. (1996). “AProbability-Based Approach to VLSI Circuit Partitioning.” In Design Automation Conference, pp. 100-105.

  • Fiduccia, C. and R. Mattheyses. (1982). “A Linear Time Heuristics for Improving Network Partitions.” In 19th ACM/IEEE Design Automation Conference, pp. 175-181.

  • Fukunaga, A.S., J.H. Huang, and A.B. Kahng. (1996). “On Clustered Kick Moves for Iterated-Descent Netlist Partitioning.” In IEEE Int'l Symp. on Circuits and Systems, vol. 4, pp. 496–499.

    Google Scholar 

  • Garey, M. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco: Freeman.

    Google Scholar 

  • Glover, F. (1989). “Tabu search-Part I.” ORSA Journal on Computing 1, 190–206.

    Google Scholar 

  • Goldberg, D. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley.

  • Hagen, L., J.H. Huang, and A.B. Kahng. (1997). “On Implementation Choices for Iterative Improvement Partitioning Algorithms.” IEEE Trans. on Computer-Aided Design 16(10), 1199–1205.

    Google Scholar 

  • Hendrickson, B. and R. Leland. (1994). “The Chaco User's Guide.” Technical Report SAND94-2692, SANDIA Nat'l Laboratory, Albuquerque, N.M.

    Google Scholar 

  • Holland, J. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press.

  • Hong, I., A.B. Kahng, and B.R. Moon. (1997). “Improved Large-Step Markov Chain Variants for the Symmetric TSP.” Journal of Heuristics 3(1), 63–81.

    Google Scholar 

  • Johnson, D.S., C. Aragon, L. McGeoch, and C. Schevon. (1989). “Optimization by Simulated Annealing: An Experimental Evaluation, Part 1, Graph Partitioning.” Operations Research 37, 865–892.

    Google Scholar 

  • Karypis, G. and V. Kumar. (1995). “A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs.” Technical Report 95-035, Univ. of Minnesota, Dept. of Computer Science.

  • Kernighan, B. and S. Lin. (1970). “An Efficient Heuristic Procedure for Partitioning Graphs.” Bell Systems Technical Journal 49, 291–307.

    Google Scholar 

  • Kirkpatrick, S., C.D. Jr. Gelatt, and M.P. Vecchi. (1983). “Optimization by Simulated Annealing.” Science 220(4598), 671–680.

    Google Scholar 

  • Krishnamurthy, B. (1984). “An Improved Min-Cut Algorithm for Partitioning VLSI Networks.” IEEE Trans. on Computers C-33, 438–446.

    Google Scholar 

  • Laszewski, G. (1991). “Intelligent Structural Operators for the k-Way Graph Partitioning Problem.” In Fourth International Conference on Genetic Algorithms, pp. 45-52.

  • Lim, A. and Y.M. Chee. (1991). “Graph Partitioning using Tabu Search.” In IEEE Int'l Symp. Circuits and Systems, pp. 1164-1167.

  • Martin, O.C., S.W. Otto, and E.W. Felten. (1991). “Large-Step Markov Chains for the Traveling Salesman Problem.” Complex Systems 5(3), 299–326.

    Google Scholar 

  • Merz, P. and B. Freisleben. (2000). “Fitness Landscapes, Memetic Algorithms, and Greedy Operators for Graph Bipartitioning.” Evolutionary Computation 8(1), 61–91.

    Google Scholar 

  • Monien, B. and R. Diekmann. (1997). “A Local Graph Partitioning Heuristic Meeting Bisection Bounds.” In Proc. 8th SIAM Conf. Parallel Processing for Scientific Computing.

  • Pellegrini, F. and J. Roman. (1996). “Scotch: A Software Package for Static Mapping by Dual Recursive Bipartitioning of Process and Architecture Graphs.” In Proc. HPCN '96 Brussels, April, pp. 493-498.

  • Preis, R. and R. Diekmann. (1996). “The Party Partitioning Library, User Guide.” Technical Report TR-RSFB-96-024, Univ. of Paderborn, Germany.

    Google Scholar 

  • Rolland, E., H. Pirkul, and F. Glover. (1996). “A Tabu Search for Graph Partitioning.” Annals of Operations Research 63.

  • Roy, K. and C. Sechen. (1993). “ATiming-Driven N-Way Chip and Multi-Chip Partitioner.” In IEEE International Conference on Computer-Aided Design, pp. 240-247.

  • Rutenbar, R. (1989). “Simulated Annealing Algorithms: An Overview.” IEEE Circuit and Devices Magazine 5(1), 19–26.

    Google Scholar 

  • Saab, Y. and V. Rao. (1990). “Stochastic Evolution:AFast Effective Heuristic for Some Genetic Layout Problems.” In 27th ACM/IEEE Design Automation Conference, pp. 26-31.

  • Sedgewick, R. and P. Flajolet. (1996). An Introduction to the Analysis of Algorithms. Addison Wesley.

  • Shim, K. (1993). Advanced Query Optimization Techniques for Relational Database Systems. Ph.D. thesis, University of Maryland, College Park, MD.

    Google Scholar 

  • Steenbeek, A.G., E. Marchiori, and A.E. Eiben. (1998). “Finding Balanced Graph Bi-Partitions Using a Hybrid Genetic Algorithm.” In IEEE International Conference on Evolutionary Computation, pp. 90-95.

  • Tao, L., Y.C. Zhao, K. Thulasiraman, and M.N.S. Swamy. (1991). “An Efficient Tabu search Algorithm for Graph Bisectioning.” In Great Lakes Symp. VLSI, pp. 92-95.

  • Yao, A.C. (1985). “Uniform Hashing Is Optimal.” Journal of the ACM 32(3), 687–693.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science & Engineering, Seoul National University, Shillim-dong, Kwanak-gu, Seoul, 151-742, Korea

    Yong-Hyuk Kim & Byung-Ro Moon

Authors
  1. Yong-Hyuk Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Byung-Ro Moon
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, YH., Moon, BR. Lock-Gain Based Graph Partitioning. Journal of Heuristics 10, 37–57 (2004). https://doi.org/10.1023/B:HEUR.0000019985.94952.eb

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:HEUR.0000019985.94952.eb

Search

Navigation