Users are often faced with the problem of finding complementary items that together achieve a single common goal (e.g., a starter kit for a novice astronomer, a collection of question/answers related to low-carb nutrition, a set of places to visit on holidays). In this paper, we argue that for some application scenarios returning item bundles is more appropriate than ranked lists. Thus we define composite retrieval as the problem of finding k bundles of complementary items. Beyond complementarity of items, the bundles must be valid w.r.t. a given budget, and the answer set of k bundles must exhibit diversity. We formally define the problem and characterize its complexity. We prove that the problem in its general form is NP-hard and that also the special cases in which each bundle is formed by only one item, or only one bundle is sought, are hard. Our characterization however suggests us how to adopt a two-phase approach (Produce-and-Choose, or PAC) in which we first produce many valid bundles, and then we choose k among them. For the first phase we devise two ad-hoc clustering algorithms, while for the second phase we adapt heuristics with approximation guarantees. We also devise another approach which is based on first finding a k-clustering and then selecting a valid bundle from each of the produced clusters (Cluster-and-Pick, or CAP). We compare experimentally the proposed methods on a large real-world database of user-generated restaurant reviews from Yahoo! Local, exploring their performance under a variety of settings. Our experiments show that when diversity is highly important, CAP is the best option, while when diversity is less important, a PAC approach constructing bundles around randomly chosen pivots, is better.

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