b'@techreport{Rub97,'b'\nTITLE = {On Batcher\'s Merge Sorts as Parallel Sorting Algorithms},\nAUTHOR = {R{\\"u}b, Christine},\nLANGUAGE = {eng},\nNUMBER = {MPI-I-1997-1-012},\nINSTITUTION = {Max-Planck-Institut f{\\"u}r Informatik},\nADDRESS = {Saarbr{\\"u}cken},\nYEAR = {1997},\nDATE = {1997},\nABSTRACT = {In this paper we examine the average running times of Batcher\'s bitonic merge and Batcher\'s odd-even merge when they are used as parallel merging algorithms. It has been shown previously that the running time of odd-even merge can be upper bounded by a function of the maximal rank difference for elements in the two input sequences. Here we give an almost matching lower bound for odd-even merge as well as a similar upper bound for (a special version of) bitonic merge. >From this follows that the average running time of odd-even merge (bitonic merge) is $\\Theta((n/p)(1+\\log(1+p^2/n)))$ ($O((n/p)(1+\\log(1+p^2/n)))$, resp.) where $n$ is the size of the input and $p$ is the number of processors used. Using these results we then show that the average running times of odd-even merge sort and bitonic merge sort are $O((n/p)(\\log n + (\\log(1+p^2/n))^2))$, that is, the two algorithms are optimal on the average if $n\\geq p^2/2^{\\sqrt{\\log p}}$. The derived bounds do not allow to compare the two sorting algorithms program, for various sizes of input and numbers of processors.},\nTYPE = {Research Report / Max-Planck-Institut f\xc3\xbcr Informatik},\n}\n'