Broadcasting is known to be an efficient means of disseminating data in wireless communication environments (such as Satellite, mobile phone networks,...). It has been recently observed that the average service time of broadcast systems can be considerably improved by taking into consideration existing correlations between requests. We study a pull-based data broadcast system where users request possibly overlapping sets of items; a request is served when all its requested items are downloaded. We aim at minimizing the average user perceived latency, i.e. the average flow time of the requests. We first show that any algorithm that ignores the dependencies can yield arbitrary bad performances with respect to the optimum even if it is given arbitrary extra resources. We then design a $(4+ε)$-speed $O(1+1/ε^2)$-competitive algorithm for this setting that consists in 1) splitting evenly the bandwidth among each requested set and in 2) broadcasting arbitrarily the items still missing in each set into the bandwidth the set has received. Our algorithm presents several interesting features: it is simple to implement, non-clairvoyant, fair to users so that no user may starve for a long period of time, and guarantees good performances in presence of correlations between user requests (without any change in the broadcast protocol). We also present a $ (4+ε)$-speed $O(1+1/ε^3)$-competitive algorithm which broadcasts at most one item at any given time and preempts each item broadcast at most once on average. As a side result of our analysis, we design a competitive algorithm for a particular setting of non-clairvoyant job scheduling with dependencies, which might be of independent interest.