The majority of recommender systems are designed to recommend items (such as movies and products) to users. We focus on the problem of recommending buyers to sellers which comes with new challenges: (1) constraints on the number of recommendations buyers are part of before they become overwhelmed, (2) constraints on the number of recommendations sellers receive within their budget, and (3) constraints on the set of buyers that sellers want to receive (e.g., no more than two people from the same household). We propose the following critical problems of recommending buyers to sellers: Constrained Recommendation (C-REC) capturing the first two challenges, and Conflict-Aware Constrained Recommendation (CAC-REC) capturing all three challenges at the same time. We show that C-REC can be modeled using linear programming and can be efficiently solved using modern solvers. On the other hand, we show that CAC-REC is NP-hard. We propose two approximate algorithms to solve CAC-REC and show that they achieve close to optimal solutions via comprehensive experiments using real-world datasets.
RBS is related to the task of constraint-based recommendation (cf. @cite_7 @cite_10 @cite_8 @cite_16 @cite_21 @cite_4 @cite_2 ).
@cite_4 @cite_7 @cite_8 @cite_21 @cite_2 @cite_16 @cite_10
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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, several applications can benefit from a system capable of recommending packages of items, in the form of sets. Sample applications 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 number of tweets. In these contexts, there is a need for a system that can recommend 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 system, focusing on different domains, as well as to information sources which can provide the cost associated with each item. Because the problem of generating the top recommendation (package) is NP-complete, we devise several approximation algorithms for generating top-k packages as recommendations. We analyze their efficiency as well as approximation quality. Finally, using two real and two synthetic data sets, we subject our algorithms to thorough experimentation and empirical analysis. Our findings attest to the efficiency and quality of our approximation algorithms for top-k packages compared to exact algorithms. Recommender systems support users in identifying products and services in e-commerce and other information-rich environments. Recommendation problems have a long history as a successful AI application area, with substantial interest beginning in the mid-1990s, and increasing with the subsequent rise of e-commerce. Recommender systems research long focused on recommending only simple products such as movies or books; constraint-based recommendation now receives increasing attention due to the capability of recommending complex products and services. In this paper, we first introduce a taxonomy of recommendation knowledge sources and algorithmic approaches. We then go on to discuss the most prevalent techniques of constraint-based recommendation and outline open research issues. Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. Most previous works have set the problem up as using a paper as a query to independently "retrieve" a set of reviewers that should review the paper. A more appropriate formulation of the problem would be to simultaneously optimize the assignments of all the papers to an entire committee of reviewers under constraints such as the review quota. In this paper, we solve the problem of committee review assignment with multi-aspect expertise matching by casting it as an integer linear programming problem. The proposed algorithm can naturally accommodate any probabilistic or deterministic method for modeling multiple aspects to automate committee review assignments. Evaluation using an existing data set shows that the proposed algorithm is effective for committee review assignments based on multi-aspect expertise matching. We study the problem of making recommendations when the objects to be recommended must also satisfy constraints or requirements. In particular, we focus on course recommendations: the courses taken by a student must satisfy requirements (e.g., take two out of a set of five math courses) in order for the student to graduate. Our work is done in the context of the CourseRank system, used by students to plan their academic program at Stanford University. Our goal is to recommend to these students courses that not only help satisfy constraints, but that are also desirable (e.g., popular or taken by similar students). We develop increasingly expressive models for course requirements, and present a variety of schemes for both checking if the requirements are satisfied, and for making recommendations that take into account the requirements. We show that some types of requirements are inherently expensive to check, and we present exact, as well as heuristic techniques, for those cases. Although our work is specific to course requirements, it provides insights into the design of recommendation systems in the presence of complex constraints found in other applications. Introduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear Diophantine Equations. Algorithms for Linear Diophantine Equations. Diophantine Approximation and Basis Reduction. POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING. Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming. The Structure of Polyhedra. Polarity, and Blocking and Anti--Blocking Polyhedra. Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming. The Simplex Method. Primal--Dual, Elimination, and Relaxation Methods. Khachiyana s Method for Linear Programming. The Ellipsoid Method for Polyhedra More Generally. Further Polynomiality Results in Linear Programming. INTEGER LINEAR PROGRAMMING. Introduction to Integer Linear Programming. Estimates in Integer Linear Programming. The Complexity of Integer Linear Programming. Totally Unimodular Matrices: Fundamental Properties and Examples. Recognizing Total Unimodularity. Further Theory Related to Total Unimodularity. Integral Polyhedra and Total Dual Integrality. Cutting Planes. Further Methods in Integer Linear Programming. References. Indexes. Recommender Systems (RS) suggest useful and interesting items to users in order to increase user satisfaction and online conversion rates. They typically exploit explicit or implicit user feedback such as ratings, buying records or clickstream data and apply statistical methods to derive recommendations. This paper focuses on explicitly formulated customer requirements as the sole type of user feedback. Its contribution lies in comparing different techniques such as knowledge- and utility-based methods, collaborative filtering, association rule mining as well as hybrid variants when user models consist solely of explicit customer requirements. We examine how this type of user feedback can be exploited for personalization in e-commerce scenarios. Furthermore, examples of actual online shops are developed where such contextual user information is available, demonstrating how more efficient RS configurations can be implemented. Results indicate that, especially for new users, explicit customer requirements are a useful source of feedback for personalization and hybrid configurations of collaborative and knowledge-based techniques achieve best results.