The Pattern Matching problem with Swaps consists in finding all occurrences of a pattern P in a text T , when disjoint local swaps in the pattern are allowed. In the Approximate Pattern Matching problem with Swaps one seeks, for every text location with a swapped match of P , the number of swaps necessary to obtain a match at the location. In this paper, we present a new approach for solving both the Swap Matching problem and the Approximate Swap Matching problem in linear time, in the case of short patterns. In particular, we devise a $\mathcal{O}(nm)$ general algorithm, named Cross-Sampling , and show an efficient implementation of it, based on bit-parallelism, which achieves $\mathcal{O}(n)$ worst-case time and $\mathcal{O}(\sigma)$-space complexity, with patterns whose length is comparable to the word-size of the target machine.