• Journal of the Korea Society of Computer and Information
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• v.20 no.5
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• pp.107-112
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• 2015

This paper proposes a simplified algorithm devised to obtain optimal solution to the marriage problem. In solving this problem, the most widely resorted to is the Gale-Shapley algorithm with the time complexity of $O({\mid}V{\mid}^2{\mid}E{\mid})$. The proposed algorithm on the other hand firstly constructs a $p_{ij}$ matrix of inter-preference sum both sexes' preference over the opposite sex. Secondly, it selects $_{min}p_i$ from each row to establish ${\mid}p_{.j}{\mid}{\geq}2,j{\in}S$, ${\mid}p_{.j}{\mid}=1$, $j{\in}H$, ${\mid}p_{.j}{\mid}=0$, $j{\in}T$. Finally, it shifts $_{min}\{_{min}p_{ST},p_{SH}+p_{HT\}$ for $_{min}P_{ST}$ of $S{\rightarrow}T$ and $p_{SH}+p_{HT}$, $p_{HT}<_{min}p_{ST}$ of $S{\rightarrow}H$, $H{\rightarrow}T$. The proposed algorithm has not only improved the Gale-Shapley's algorithm's complexity of $O({\mid}V{\mid}^2{\mid}E{\mid})$ to $O({\mid}V{\mid}^2)$ but also proved its extendable use on unbalanced marriage problems.