Graph partitioning method based on connected graph constrained knapsack problem

Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering

Volumn 32, Issue 10, 2012, Pages 134-141

  Lin, Jikeng ^a   Wang, Xudong ^b   Li, Shengwen ^a   Wu, Peng ^a   Shao, Guanghui ^c   Xu, Xingwei ^c   Ma, Xin ^c  

^a TIANJIN UNIVERSITY   (China)

^b Technology Center of Tianjin Electrical Power Cooperation   (China)

^c Northeast Electric Power Dispatching Center   (China)

Author keywords

Approximation algorithm; Connected graph constrained knapsack problem (CGKP); Graph constrained knapsack problem (GKP); Graph partition; Optimal controlled partition of power system

Indexed keywords

APPROXIMATION ALGORITHMS; COMBINATORIAL OPTIMIZATION; GRAPH THEORY; OPTIMIZATION; STANDBY POWER SYSTEMS;

COMPUTATION COMPLEXITY; CONNECTED GRAPH; EFFICIENT APPROXIMATION ALGORITHMS; GRAPH CONNECTIVITY; GRAPH PARTITION; GRAPH PARTITION PROBLEM; GRAPH PARTITIONING; KNAPSACK PROBLEMS; NODE SETS; POWER GRIDS; SEARCHING METHODS;

INTEGER PROGRAMMING;

EID: 84860571909     PISSN: 02588013     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. Lu Kaicheng, Lu Huaming. Graph theory and applications [M]. 2nd ed. Beijing: Tsinghua University Press, 2004: 3-4(in Chinese).
2. Ji Guishu, Lu Zhiyuan, Li Qingchun. A new method for the minimum cut problem [J]. Computer Engineering and Applications, 2003(2): 98-100(in Chinese).
3. Poljak S, Rendl F. Solving the max-cut problem using eigenvalues [J]. Discrete Applied Mathematics, 1995(62): 249-278.
4. Coemans M X, Williamson D P. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming [J]. ACM, 1995, 42(6): 1115-1145.
5. Bryant R E. Symbolic Boolean manipulation with ordered binary decision diagrams [J]. ACM Computing Surveys, 1992, 24(3): 293-318.
6. Bryant R E. Graph-based algorithms for Boolean function manipulation [J]. IEEE Transactions on Computers, 1986, 35(8): 677-691.
7. Chan P K, Schlag M D F, Zien J Y. Spectral K-way ratio-cut partitioning and clustering [J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1994, 13(9): 1088-1096.
8. Karypis G, Kumar V. Analysis of multilevel graph partitioning [R]. Minnesota, USA: University of Minnesota, 1995.
9. Gilbert J R, Miller G L, Teng S H. Geometric mesh partitioning: implementation and experiments [C]//Proceedings of 9th International Parallel Processing Symposium. Santa Barbara, CA, USA: Institute of Electrical and Electronics Engineers, 2003: 418-427.
10. Karypis G. METIS: a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices version 5.0 [EB/OL]. 2011-04 [2011-12-10]. http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/manual.pdf.
11. Stephen T B, Horst D S. A fast meltilevel implementation of recusive spectral bisection unstructured problems [C]//The Sixth SIAM Conference on Parallel Processing for Scientific Computing. Norfolk, Virginia, USA: ACM, 1993: 711-718.
12. Kleinberg J M. Authoritative sources in a hyperlinked environment [J]. Journal of the ACM, 1999, 46(5): 604-632.
13. Girvan M, Newman M E J. Community structure in social and biological networks [J]. Proceedings of the National Academy of Science, 2002, 99(12): 7821-7826.
14. Radicchi F, Castellano C, Cecconi F, et al. Defining and identifying communities in networks [J]. Proceedings of the National Academy of Science, 2004, 101(9): 2658-2663.
15. Roberto S O. 2-approximation algorithm for finding a spanning tree with maximum number of leaves [C]//Proceeding ESA'98 Proceedings of the 6th Annual European Symposium on Algorithms. London, UK: Springer-Verlag, 1998: 441-452.
16. Guha S, Khuller S. Improved methods for approximating node weighted steiner trees and connected dominating sets [J]. Information and Computation, 1999, 150(1): 57-74.
17. Prim R C. Shortest connection networks and some generalizations [J]. Bell System Technical Journal, 1957(36): 1389-1401.
18. Borradaile G, Heeringa B, Wilfong G. Approximation algorithms for constrained knapsack problems [EB/OL]. 2009-04 [2011-12-10]. http://citeseerx.ist.psu.edu/viewdoc/download? doi=10.1.1.147.6878&rep=rep1&type=pdf.