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.
Review assignment is a common task that many people such as conference organizers, journal editors, and grant administrators would have to do routinely. As a computational problem, it involves matching a set of candidate reviewers with a paper or proposal to be reviewed. A common deficiency of all existing work on solving this problem is that they do not consider the multiple aspects of topics or expertise and all match the entire document to be reviewed with the overall expertise of a reviewer. As a result, if a document contains multiple subtopics, which often happens, existing methods would not attempt to assign reviewers to cover all the subtopics; instead, it is quite possible that all the assigned reviewers would cover the major subtopic quite well, but not covering any other subtopic. In this paper, we study how to model multiple aspects of expertise and assign reviewers so that they together can cover all subtopics in the document well. We propose three general strategies for solving this problem and propose new evaluation measures for this task. We also create a multi-aspect review assignment test set using ACM SIGIR publications. Experiment results on this data set show that the proposed methods are effective for assigning reviewers to cover all topical aspects of a document. 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.  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.