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.
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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
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