On Sorting Multiple Bitonic Sequences

Bitonic sorters sort a single bitonic sequence into an ascending sequence. A multi-bitonic sorter is presented here, which sorts k bitonic sequences of n keys each into an ascending sequence in at most left( {leftlceil {log _2 left( {k + leftlceil {frac{k} {2}} rightrceil } right)} rightrceil + 1} right)left( {leftlceil {log _2 n} rightrceil - 1} right)+T(1,k)+leftlceil {log _2 k} rightrceil +1 time delay, where T(1,k) is the time delay needed to sort k keys in order; and k is any integer not restricted to 1.