A finite-time convergent recurrent neural network based algorithm for the L smallest k-subsets sum problem

Authors:
Shenshen Gu
Affiliations:
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, P.R. China
Venue:
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part I
Year:
2013

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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 Lk-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.