Traditional database queries follow a simple model: they define constraints that each tuple in the result must satisfy. This model is computationally efficient, as the database system can evaluate the query conditions on each tuple individually. However, many practical, real-world problems require a collection of result tuples to satisfy constraints collectively, rather than individually. In this paper, we present package queries, a new query model that extends traditional database queries to handle complex constraints and preferences over answer sets. We develop a full-fledged package query system, implemented on top of a traditional database engine. Our work makes several contributions. First, we design PaQL, a SQL-based query language that supports the declarative specification of package queries. We prove that PaQL is as least as expressive as integer linear programming, and therefore, evaluation of package queries is in general NP-hard. Second, we present a fundamental evaluation strategy that combines the capabilities of databases and constraint optimization solvers to derive solutions to package queries. The core of our approach is a set of translation rules that transform a package query to an integer linear program. Third, we introduce an offline data partitioning strategy allowing query evaluation to scale to large data sizes. Fourth, we introduce SKETCHREFINE, a scalable algorithm for package evaluation, with strong approximation guarantees ((1 ± ε) 6 -factor approximation). Finally, we present extensive experiments over real-world and benchmark data. The results demonstrate that SKETCHREFINE is effective at deriving high-quality package results, and achieves runtime performance that is an order of magnitude faster than directly using ILP solvers over large datasets.
Documents and queries are rich in temporal features, both at the meta-level and at the content-level. We exploit this information to define temporal scope similarities between documents and queries in metric spaces. Our experiments show that the proposed metrics can be very effective for modeling the relevance for different search tasks, and provide insights into an inherent asymmetry in temporal query semantics. Moreover, we propose a simple ranking model that combines the temporal scope similarity with traditional keyword similarities. We experimentally show that it is not worse than traditional keywordbased rankings for non-temporal queries, and that it improves the overall effectiveness for time-based queries.
Recommendation systems aim to identify items that are likely to be of interest to users. In many cases, users are interested in package recommendations as collections of items. For example, a dietitian may wish to derive a dietary plan as a collection of recipes that is nutritionally balanced, and a travel agent may want to produce a vacation package as a coordinated collection of travel and hotel reservations. Recent work has explored extending recommendation systems to support packages of items. These systems need to solve complex combinatorial problems, enforcing various properties and constraints defined on sets of items. Introducing constraints on packages makes recommendation queries harder to evaluate, but also harder to express: Queries that are under-specified produce too many answers, whereas queries that are over-specified frequently miss interesting solutions.In this paper, we study query relaxation techniques that target package recommendation systems. Our work offers three key insights: First, even when the original query result is not empty, relaxing constraints can produce preferable solutions. Second, a solution due to relaxation can only be preferred if it improves some property specified by the query. Third, relaxation should not treat all constraints as equals: some constraints are more important to the users than others. Our contributions are threefold: (a) we define the problem of deriving package recommendations through query relaxation, (b) we design and experimentally evaluate heuristics that relax query constraints to derive interesting packages, and (c) we present a crowd study that evaluates the sensitivity of real users to different kinds of constraints and demonstrates that query relaxation is a powerful tool in diversifying package recommendations.
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