We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes seemingly different problems that had been studied in isolation. To this end, we extend classic algorithms that find the k-shortest paths in a weighted graph. For full conjunctive queries, including cyclic ones, our approach is optimal in terms of the time to return the top result and the delay between results. These optimality properties are derived for the widely used notion of data complexity, which treats query size as a constant. By performing a careful cost analysis, we are able to uncover a previously unknown tradeoff between two incomparable enumeration approaches: one has lower complexity when the number of returned results is small, the other when the number is very large. We theoretically and empirically demonstrate the superiority of our techniques over batch algorithms, which produce the full result and then sort it. Our technique is not only faster for returning the first few results, but on some inputs beats the batch algorithm even when all results are produced.

中文翻译：

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全连接查询答案排序枚举的最优算法

我们根据由选择性二元组定义的非常一般的顺序研究连接查询结果的排序枚举。我们的主要贡献是对一类动态规划问题进行排序枚举的框架，该框架概括了孤立研究的看似不同的问题。为此，我们扩展了在加权图中找到 k 最短路径的经典算法。对于完整的连接查询，包括循环查询，我们的方法在返回顶部结果的时间和结果之间的延迟方面是最佳的。这些最优性属性源自广泛使用的数据复杂性概念，该概念将查询大小视为常数。通过进行仔细的成本分析，我们能够发现两种无与伦比的枚举方法之间以前未知的权衡：当返回的结果数量很少时，一个复杂度较低，当数量非常大时，另一个复杂度较低。我们从理论上和经验上证明了我们的技术优于批处理算法，批处理算法产生完整的结果然后对其进行排序。我们的技术不仅在返回前几个结果方面更快，而且在某些输入上甚至在所有结果都产生时击败了批处理算法。