This paper studies the problem of finding objects with durable quality over time in historical time series databases. For example, a sociologist may be interested in the top 10 web search terms during the period of some historical events; the police may seek for vehicles that move close to a suspect 70 percent of the time during a certain time period and so on. Durable top-k (DTop-k) and nearest neighbor (DkNN) queries can be viewed as natural extensions of the standard snapshot top-k and NN queries to timestamped sequences of values or locations. Although their snapshot counterparts have been studied extensively, to our knowledge, there is little prior work that addresses this new class of durable queries. Existing methods for DTop-k processing either apply trivial solutions, or rely on domain-specific properties. Motivated by this, we propose efficient and scalable algorithms for the DTop-k and DkNN queries, based on novel indexing and query evaluation techniques. Our experiments show that the proposed algorithms outperform previous and baseline solutions by a wide margin.

Given a set of spatial points DS, each of which is associated with categorical information, e.g., restaurant, pub, etc., the optimal route query finds the shortest path that starts from the query point (e.g., a home or hotel), and covers a user-specified set of categories (e.g., {pub, restaurant, museum}). The user may also specify partial order constraints between different categories, e.g., a restaurant must be visited before a pub. Previous work has focused on a special case where the query contains the total order of all categories to be visited (e.g., museum → restaurant → pub). For the general scenario without such a total order, the only known solution reduces the problem to multiple, total-order optimal route queries. As we show in this paper, this naive approach incurs a significant amount of repeated computations, and, thus, is not scalable to large data sets. Motivated by this, we propose novel solutions to the general optimal route query, based on two different methodologies, namely backward search and forward search. In addition, we discuss how the proposed methods can be adapted to answer a variant of the optimal route queries, in which the route only needs to cover a subset of the given categories. Extensive experiments, using both real and synthetic data sets, confirm that the proposed solutions are efficient and practical, and outperform existing methods by large margins.