The following multithreaded algorithm computes transpose of a matrix in parallel:
$p\ Trans(X,Y,N)$
if $N=1$
then $Y[1,1]\leftarrow X[1,1]$
else partition $X$ into four $(N/2)\times(N/2)$ submatrices $X_{11},X_{12},X_{21},X_{22}$
partition $Y$ into four $(N/2)\times(N/2)$ submatrices $Y_{11},Y_{12},Y_{21},Y_{22}$
spawn $p\ Trans(X_{11},Y_{11},N/2)$
spawn $p\ Trans(X_{12},Y_{12},N/2)$
spawn $p\ Trans(X_{21},Y_{21},N/2)$
spawn $p\ Trans(X_{22},Y_{22},N/2)$
What is the asymptotic parallelism of the algorithm?
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