The Shapley value provides a natural means of quantifying the contributions of facts to database query answers. In this work, we seek to broaden our understanding of Shapley value computation (SVC) in the database setting by revealing how it relates to Fixed-size Generalized Model Counting (FGMC), which is the problem of computing the number of sub-databases of a given size and containing a given set of assumed facts that satisfy a fixed query. Our focus will be on explaining the difficulty of SVC via FGMC, and to this end, we identify general conditions on queries which enable reductions from FGMC to SVC. As a byproduct, we not only obtain alternative explanations for most existing results on SVC, but also new complexity results. In particular, we establish FP-#P complexity dichotomies for constant-free connected UCQs and homomorphism-closed connected graph queries. We further explore variants of SVC, either in the absence of assumed facts, or where we measure the contribution of constants rather than facts.

翻译：Shapley值提供了量化事实对数据库查询结果贡献的自然方法。本文旨在通过揭示Shapley值计算（SVC）与固定规模广义模型计数（FGMC）之间的关联，拓展我们对数据库环境下SVC的理解。FGMC是指计算满足固定查询的、包含给定假设事实且规模确定的子数据库数量问题。我们将聚焦于通过FGMC解释SVC的难度，为此确定了从FGMC到SVC的归约条件。作为副产品，我们不仅获得了对现有SVC结果的新解释，还得到了新的复杂度结论。具体而言，我们建立了无常数连通UCQ和同态闭连通图查询的FP-#P复杂度二分法。此外，我们进一步探讨了SVC的变体，包括无假设事实的情况，以及度量常数贡献而非事实贡献的情形。