We aim at providing a social network such that users form groups to practice together some activities. In this paper, we present a formal framework for coalition formation which is suitable for our usecase. We restrict ourselves to additively separable preferences whose representation is linear with respect to the inputs. We propose here a distributed algorithm which aims at maximizing the egalitarian welfare of the resulting matching. Our experiments shows that: i) this algorithm reaches a better outcome than the classical local search techniques; and ii) the distribution of our algorithm speeds up its runtime.