Abstract--Expertise matching, aiming to find the alignment between experts and queries, is a common problem in many real applications such as conference paper-reviewer assignment, product-reviewer alignment, and product-endorser matching. Most of existing methods for this problem usually find "relevant" experts for each query independently by using, e.g., an information retrieval method. However, in real-world systems, various domain-specific constraints must be considered. For example, to review a paper, it is desirable that there is at least one senior reviewer to guide the reviewing process. An important question is: "Can we design a framework to efficiently find the optimal solution for expertise matching under various constraints?" This paper explores such an approach by formulating the expertise matching problem in a constraintbased optimization framework. Interestingly, the problem can be linked to a convex cost flow problem, which guarantees an optimal solut...