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We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem Shortest Common Superstring with Reversals (SCS-R). This problem has been introduced by Jiang et al., who designed a greedy-like algorithm with length approximation ratio $4$. In this paper, we show that a natural adaptation of the classical greedy algorithm for SCS has (optimal) compression ratio $\frac12$, i.e., the sum of the overlaps in the output string is at least half the sum of the overlaps in an optimal solution. We also provide a linear-time implementation of our algorithm., Published in Information Processing Letters

The optimization versions of the k -PARTITIONING problems are considered in this paper. For the objective to maximize the minimum load of m subsets, we first show that the FOLDING algorithm has a tight worst case ratio of max{2/ k ,1/ m }. Then, we present an algorithm called HARMONIC1 with a worst case ratio at least max{ 1/ k , 1/(⌈ Σ i =1 m 1/ i ⌉ +1)}. It concludes the HARMONIC1 is better than FOLDING for k > 2(⌈ Σ i =1 m 1/i ⌉ + 1). We further show that HARMONICI is asymptotically optimal ordinal algorithm. We also present an algorithm HARMONIC2 for solving the general κ i -PARTITIONING problem.

International audience; In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence of a set of sequences (ELCS problem), a generalization of the Longest Common Subsequence problem, where the input sequences are over the union of two disjoint sets of symbols, a set of mandatory symbols and a set of optional symbols. We show that different versions of the problem are APX-hard even for instances with two sequences. Moreover, we show that the related problem of determining the existence of a feasible solution of the Exemplar Longest Common Subsequence of two sequences is NP-hard. On the positive side, we first present an efficient algorithm for the ELCS problem over instances of two sequences where each mandatory symbol can appear in total at most three times in the sequences. Furthermore, we present two fixed parameter algorithms for the ELCS problem over instances of two sequences where the parameter is the number of mandatory symbols.

International audience; String matching is the problem of finding all the occurrences of a pattern in a text. We present a new method to compute the combinatorial shift function ("matching shift") of the well-known Boyer-Moore string matching algorithm. This method implies the computation of the length of the longest suffixes of the pattern ending at each position in this pattern. These values constituted an extra-preprocessing for a variant of the Boyer-Moore algorithm designed by Apostolico and Giancarlo. We give here a new presentation of this algorithm that avoids extra preprocessing together with a tight bound of 1.5n character comparisons (where n is the length of the text).