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Bigger screening collections increase the odds of finding more and better hits. For this reason, large pharmaceutical companies have invested heavily in high-throughput screening (HTS) collections that can contain several million compounds. However, this figure pales in comparison with the emergent on-demand chemical collections, which have recently reached the trillion scale. These chemical collections are potentially transformative for drug discovery, as they could deliver many diverse and high-quality hits, even reaching lead-like starting points. But first, it will be necessary to develop computational tools capable of efficiently navigating such massive virtual collections. To address this challenge, we have conceived an innovative strategy that explores the chemical universe from the bottom up, performing a systematic search on the fragment space (exploration phase), to then mine the most promising areas of on-demand collections (exploitation phase). 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