A lower bound for sorting networks that use the divide-sort-merge strategy

• Authors: David C. Van Voorhis
• Venue: A lower bound for sorting networks that use the divide-sort-merge strategy
• Year: 1971

Let $M_g (g^{k+1})$ represent the minimum number of comparators required by a network that merges g sorted multisets containing $g^k$ members each. In this paper we prove that $M_g (g^{k+1}) \geq\ g M_g(g^k) + g^{k-1} \sum_{\ell =2}^{g} \lfloor (\ell -1)g/\ell\rfloor$. From this relation we are able to show that an N-sorter network which uses the g-way divide-sort-merge strategy must contain at least order $N{(log_2 N)}^2$ comparators.