Front. Comput. Sci., 2012, 6(3): 264–277 DOI 10.1007/s11704-012-2014-1 Composite recommendations: from items to packages Min XIE 1 , Laks V. S. LAKSHMANAN 1 , Peter T. WOOD 2 1 Department of Computer Science, University of British Columbia, Vancouver, V6T 1Z4, Canada 2 Department of Computer Science and Information Systems, Birkbeck, University of London, London, WC1E 7HX, UK c  Higher Education Press and Springer-Verlag Berlin Heidelberg 2012 Abstract Classical recommender systems provide users with a list of recommendations where each recommendation consists of a single item, e.g., a book or DVD. However, sev- eral applications can benefit from a system capable of recom- mending packages of items, in the form of sets. Sample appli- cations include travel planning with a limited budget (price or time) and twitter users wanting to select worthwhile tweeters to follow, given that they can deal with only a bounded num- ber of tweets. In these contexts, there is a need for a system that can recommend the top-k packages for the user to choose from. Motivated by these applications, we consider composite recommendations, where each recommendation comprises a set of items. Each item has both a value (rating) and a cost associated with it, and the user specifies a maximum total cost (budget) for any recommended set of items. Our composite recommender system has access to one or more component recommender systems focusing on different do- mains, as well as to information sources which can provide the cost associated with each item. Because the problem of deciding whether there is a recommendation (package) whose cost is under a given budget and whose value exceeds some threshold is NP-complete, we devise several approximation algorithms for generating the top-k packages as recommen- dations. We analyze the efficiency as well as approximation quality of these algorithms. Finally, using two real and two synthetic datasets, we subject our algorithms to thorough ex- perimentation and empirical analysis. Our findings attest to Received January 11, 2012; accepted February 2, 2012 E-mail: minxie@cs.ubc.ca the efficiency and quality of our approximation algorithms for the top-k packages compared to exact algorithms. Keywords recommendation algorithms, optimization, top-k query processing 1 Introduction Recommender systems (RecSys) have become very popular of late and have become an essential driver of many appli- cations including web services [1]. However, classical Rec- Sys provide recommendations consisting of single items, e.g., books or DVDs. Several applications can benefit from a sys- tem capable of recommending packages of items, in the form of sets. For example, in trip planning, a user is interested in suggestions for places to visit, or points of interest (POI). There may be a cost associated with each visiting place (time, price, etc.). Optionally, there may be a notion of compatibility among items in a set, modeled in the form of constraints: e.g., “no more than three museums in a package”, “not more than two parks”, “the total distance covered in visiting all POIs in a package should be  10 km”. The user may have a limited budget and may be interested in suggestions of compatible sets of POIs such that the cost of each set is within budget and has a value (as judged from ratings) that is as high as possible. In these applications, there is a natural need for the top-k recommendation packages for the user to choose from. Some so-called “third generation” travel planning web sites, such as NileGuide 1) and YourTour 2) , are starting to provide some of these features, although in a limited form. Another application arises in social networks, like twitter, 1) http://www.nileguide.com 2) http://www.yourtour.com