Randomized Swap Matching in $O(m \log m \log

We give a randomized algorithm for the {\em Pattern Matching with Swaps} problem which runs in $O(m \log m \log |\Sigma| )$ time on a text of length $2m-1$ and a pattern of length $m$ drawn from an alphabet set of size $|\Sigma|$. This algorithm gives the correct answer with probability at least $1-\frac{1}{m}$ and does not miss a match. The best deterministic algorithm known for this problem takes $O(m^{4/3} \mbox{polylog}(m))$ time.