Conjunctive Regular Path Queries, or CRPQs for short, are an essential construct in graph query languages. In this paper, we propose the first output-sensitive algorithm for evaluating acyclic CRPQs. It is output-sensitive in the sense that its complexity is a function of the sizes of the input graph and of the query output. In particular, it does not depend on the output sizes of the regular expressions that appear in the query, as these sizes can be much larger than the query output size. Our algorithm proceeds in two stages. In the first stage, it contracts the given query into a free-connex acyclic one such that the output of the original query can be obtained from the output of the contracted one. This contraction removes bound variables by composing regular expressions or by promoting bound variables to free ones. The minimum necessary number of promoted bound variables gives the contraction width, which is a novel parameter specific to CRPQs. In the second stage, our algorithm evaluates the free-connex acyclic CRPQ and projects away the columns of the promoted bound variables. It ensures output-sensitivity by computing the calibrated outputs of the regular expressions appearing in the free-connex acyclic CRPQ in time proportional to their sizes. Our algorithm has lower complexity than the state-of-the-art approaches for problem instances where (i) the query output is asymptotically smaller than the worst-case output size or (ii) the largest output size of any of the regular expression in the query.

翻译：合取正则路径查询（简称CRPQ）是图查询语言中的核心构造。本文提出了首个用于评估无环CRPQ的输出敏感算法。其输出敏感性体现在算法复杂度取决于输入图与查询输出的大小，特别地，它不依赖于查询中正则表达式的输出规模——这些规模可能远大于查询输出规模。我们的算法分为两个阶段：第一阶段将给定查询压缩为自由连通无环查询，使得原始查询的输出可通过压缩查询的输出获得。该压缩过程通过组合正则表达式或将绑定变量提升为自由变量来消除绑定变量。必须提升的最小绑定变量数量定义了压缩宽度，这是CRPQ特有的新参数。第二阶段，算法评估自由连通无环CRPQ并投影掉提升绑定变量对应的列。通过以正比于表达式规模的时间计算自由连通无环CRPQ中正则表达式的校准输出，算法确保了输出敏感性。对于以下两类问题实例，本算法具有低于现有最优方法的复杂度：(i) 查询输出渐近小于最坏情况输出规模；(ii) 查询中任意正则表达式的最大输出规模较大。