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As data analytics becomes more crucial to digital systems, so grows theimportance of characterizing the database queries that admit a more efficientevaluation. We consider the tractability yardstick of answer enumeration with apolylogarithmic delay after a linear-time preprocessing phase. Such anevaluation is obtained by constructing, in the preprocessing phase, a datastructure that supports polylogarithmic-delay enumeration. In this paper, weseek a structure that supports the more demanding task of a "randompermutation": polylogarithmic-delay enumeration in truly random order.Enumeration of this kind is required if downstream applications assume that theintermediate results are representative of the whole result set in astatistically valuable manner. An even more demanding task is that of a "randomaccess": polylogarithmic-time retrieval of an answer whose position is given.  We establish that the free-connex acyclic CQs are tractable in all threesenses: enumeration, random-order enumeration, and random access; and in theabsence of self-joins, it follows from past results that every other CQ isintractable by each of the three (under some fine-grained complexityassumptions). However, the three yardsticks are separated in the case of aunion of CQs (UCQ): while a union of free-connex acyclic CQs has a tractableenumeration, it may (provably) admit no random access. For such UCQs we devisea random-order enumeration whose delay is logarithmic in expectation. We alsoidentify a subclass of UCQs for which we can provide random access withpolylogarithmic access time. Finally, we present an implementation and anempirical study that show a considerable practical superiority of ourrandom-order enumeration approach over state-of-the-art alternatives.

Answering (Unions of) Conjunctive Queries using Random Access and Random-Order Enumeration