Abstract. In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using the model, we devise two efficient algorithms to solve the swap matching problem. The resulting algorithms are adaptations of the classic shift-and algorithm. For patterns having length similar to the word-size of the target machine, both the algorithms run in linear time considering a fixed alphabet.

An algorithm to determine whether or not a given array is a Lyndon array.• Two algorithms to compute a string from a valid Lyndon array.• An algorithm to compute a unique string from "rotated" Lyndon arrays.• Plus theoretical background.

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In this paper, we present a novel approximation algorithm to solve the protein folding problem in HP model. Our algorithm is polynomial in terms of the length of the given HP string. The expected approximation ratio of our algorithm is 1-2lognn-1 for n ≥ 6, where n2 is the total number of H’s in a given HP string. The expected approximation ratio tends to reach 1 for large values of n. Hence our algorithm is expected to perform very well for larger HP strings.

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