This article is interested in the problem of the linguistic content of a speech corpus. Depending on the target task, the phonological and linguistic content of the corpus is controlled by collecting a set of sentences which covers a preset description of phonological attributes under the constraint of an overall duration as small as possible. This goal is classically achieved by greedy algorithms which however do not guarantee the optimality of the desired cover. In recent works, a lagrangian-based algorithm, called LamSCP, has been used to extract coverings of diphonemes from a large corpus in French, giving better results than a greedy algorithm. We propose to keep comparing both algorithms in terms of the shortest duration, stability and robustness by achieving multi-represented diphoneme or triphoneme covering. These coverings correspond to very large scale optimization problems, from a corpus in English. For each experiment, LamSCP improves the greedy results from 3.9 to 9.7 per...