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International Symposium on Neural Networks

ISNN 2013: Advances in Neural Networks – ISNN 2013 pp 19–27Cite as

A Finite-Time Convergent Recurrent Neural Network Based Algorithm for the L Smallest k-Subsets Sum Problem

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7951)

Abstract

For a given set S of n real numbers, a k-subset means a subset of k distinct elements of S. It is obvious that there are totally \(C_{n}^{k}\) different combinations. The L smallest k-subsets sum problem is defined as finding L k-subsets whose summation of subset elements are the L smallest among all possible combinations. This problem has many applications in research and the real world. However the problem is very computationally challenging. In this paper, a novel algorithm is proposed to solve this problem. By expressing all the \(C_{n}^{k}\) k-subsets with a network, the problem is converted to finding the L shortest loopless paths in this network. By combining the L shortest paths algorithm and the finite-time convergent recurrent neural network, a new algorithm for the L smallest k-subsets problem is developed. And experimental results show that the proposed algorithm is very effective and efficient.

Keywords

  • L smallest k-subsets sum problem
  • L shortest paths
  • convergence in finite time
  • recurrent neural network

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References

  1. Nijenhuis, A., Wilf, H.: Combinatorial Algorithms for Computers and Calculators, 2nd ed. Academic Press, New York (1978)

    Google Scholar 

  2. Wang, H., Ma, Z., Nakayama, I.: Effectiveness of penalty function in solving the subset sum problem. In: Proceedings of IEEE International Conference on Evolutionary Computation, pp. 422–425 (1996)

    Google Scholar 

  3. Bocus, M.Z., Coon, J.P., Canagarajah, C.N., Armour, S.M.D., Doufexi, A., McGeehan, J.P.: Per-Subcarrier Antenna Selection for H.264 MGS/CGS Video Transmission Over Cognitive Radio Networks. IEEE Transactions on Vehicular Technology 61(3), 1060–1073 (2012)

    CrossRef  Google Scholar 

  4. Choi, H., Kim, J., Yoon, C.W., Park, I.C., Hwang, S.H., Kyung, C.H.: Synthesis of application specific instructions for embedded DSP software. IEEE Transactions on Computers 48(6), 603–614 (1999)

    CrossRef  Google Scholar 

  5. Martello, S., Toth, P.: 4 Subset-sum problem. In: Knapsack Problems: Algorithms and Computer Interpretations, pp. 105–136. Wiley-Interscience (1990)

    Google Scholar 

  6. Lagarias, J.C., Odlyzko, A.M.: Solving low density subset sum problems. In: 24th Annual Symposium on Foundations of Computer Science, pp. 1–10 (1983)

    Google Scholar 

  7. Lobstein, A.: The hardness of solving subset sum with preprocessing. IEEE Transactions on Information Theory 36(4), 943–946 (1990)

    MathSciNet  MATH  CrossRef  Google Scholar 

  8. Chang, W.L., et al.: Quantum Algorithms of the Subset-Sum Problem on a Quantum Computer. In: WASE International Conference on Information Engineering, ICIE 2009, pp. 54–57 (2009)

    Google Scholar 

  9. Mine, T., Murakami, Y.: An implementation of space-time tradeoff method for subset sum problem. In: 6th International Conference on Computer Sciences and Convergence Information Technology (ICCIT), pp. 618–621 (2011)

    Google Scholar 

  10. Liu, S., Wang, J.: A simplified dual neural network for quadratic programming with its KWTA application. IEEE Transactions on Neural Networks 17(6), 1500–1510 (2006)

    CrossRef  Google Scholar 

  11. Gu, S.S., Wang, J.: A K-Winners-Take-All Neural Network Based on Linear Programming Formulation. In: International Joint Conference on Neural Networks, IJCNN 2007, pp. 37–40 (2007)

    Google Scholar 

  12. Yen, J.Y.: Finding the K shortest Loopless Paths in a Network. Management Science 17(11), 712–716 (1971)

    MATH  CrossRef  Google Scholar 

  13. Liu, Q.S., Wang, J.: Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions. IEEE Transactions on Neural Networks 22(4), 601–613 (2011)

    CrossRef  Google Scholar 

  14. Wang, J.: Primal and Dual Neural Networks for Shortest-Path Routing, Systems, Man and Cybernetics. IEEE Transactions on Part A: Systems and Humans 28(6) (1998)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mechatronic Engineering and Automation, Shanghai University, 149 Yanchang Road, Shanghai, 200072, P.R. China

    Shenshen Gu

Authors
  1. Shenshen Gu
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Editor information

Editors and Affiliations

  1. School of Information and Communication Engineering, Dalian University of Technology, A 530, Chuangxinyuan Building, 116023, Dalian, China

    Chengan Guo

  2. Institute of Automation, Chinese Academy of Sciences, 100864, Beijing, China

    Zeng-Guang Hou

  3. School of Automation, Huazhong University of Science and Technology, 430074, Wuhan, China

    Zhigang Zeng

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Gu, S. (2013). A Finite-Time Convergent Recurrent Neural Network Based Algorithm for the L Smallest k-Subsets Sum Problem. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_3

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  • DOI: https://doi.org/10.1007/978-3-642-39065-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39064-7

  • Online ISBN: 978-3-642-39065-4

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