In [9] and [10], we have shown that the dynamic discovery of e-services (or web services) can be reduced to the computational problem of finding all minimal transversals with a minimal cost of a hypergraph. Here, we propose an algorithm called computeBCov to achieve this task: it is in fact the classical algorithm to generate minimal transversals of a hypergraph (given in [13]) which we have optimized and adapted. We give and theoretically study worst cases for computeBCov. We describe the D2CP prototype in which computeBCov has been implemented, and, through many tests, show how it behaves on worst cases and on generated sets of e-services.