What is the best solution for Inversion of Burrows-Wheeler Transform?One with the least number of steps.(Best solution => One with a smaller average-case or worst-case time complexity)Hopefully, a smaller time-complexity than  this one.
Inverse of Burrows-Wheeler Transform
ds.algorithms
Do you mean construction or inversion of BWT?For construction, the best algorithm is probably the one by Okanohara and Sadakane. It takes $O(n)$ time and usually requires $2n$ to $2.5n$ bytes of memory for an input of length $n$. There is an implementation available at Google code.I am not that familiar with BWT inversion algorithms. The papers of Krkkinen and Puglisi at ESA 2010 and CCP 2011 might provide a good starting point.