无环约束下合取查询的大小界
Size Bounds for CQs Under Acyclic Constraints
AI总结：
本文研究无环约束下合取查询的大小界，对比熵界与拟阵多面体界，发现允许投影时两类界存在多项式差距，并给出拟阵多面体界紧致的特殊情形。
AI中文摘要：
我们研究合取查询（Conjunctive Query, CQ）结果的大小界，这类查询近年来在数据库理论中发挥了关键作用。具体而言，我们对比两类界：一是熵界，已知其渐近紧致但不可计算；二是其可计算的松弛形式——拟阵多面体界，该界通常不紧致。本文聚焦于无环函数依赖下的合取查询，这类查询在无投影时表现良好，两类界重合。我们证明，当允许投影时，情况发生变化：即便在无环函数依赖下，两类界间通常存在多项式差距。作为对该负面结果的补充，我们给出一类特殊情形：在无环函数依赖与投影下，拟阵多面体界是紧致的，该情形由查询变量拓扑序中输出变量的位置所刻画。
英文摘要：
We study size bounds for conjunctive query (CQ) results which in recent years have played a crucial role in database theory. In particular, we compare the so-called entropic bound which is known to be asymptotically tight but not known to be computable, and its computable relaxation called the polymatroid bound, which is generally not tight. We focus here on conjunctive queries under acyclic functional dependencies. These queries are known to be well-behaved in the sense that, in the case without projections, both bounds coincide. We show that this picture changes when projections are allowed: in this case, even for acyclic functional dependencies, there is in general a polynomial gap between the two bounds. We complement this negative result by showing a special case for which the polymatroid bound is tight under acyclic functional dependencies and projections that is characterized by the position of the output variables in a topological order of the query variables.
