Time- and VLSI-optimal Sorting on Meshes with Multiple Broadcasting

In this work, we present a time-and VLSI-optimal sorting algorithm for meshes with multiple broadcasting. Specifically, we show that for every choice of a positive integer constant c, m items left( {n^{frac{1} {2} + frac{1} {{2c}}} leqslant m leqslant n} right) stored in the first leftlceil {frac{m} {{sqrt n }}} rightrceil columns of a mesh with multiple broadcasting of size sqrt {n} x sqrt {n} can be sorted in O({frac{m} {{sqrt n }}}) time.