Motivated by the common academic problem of allocating papers to referees for conference reviewing we propose a novel mechanism for solving the assignment problem when we have a two sided matching problem with preferences from one side (the agents reviewers) over the other side (the objects papers) and both sides have capacity constraints. The assignment problem is a fundamental problem in both computer science and economics with application in many areas including task and resource allocation. We draw inspiration from multi-criteria decision making and voting and use order weighted averages (OWAs) to propose a novel and flexible class of algorithms for the assignment problem. We show an algorithm for finding a @math -OWA assignment in polynomial time, in contrast to the NP-hardness of finding an egalitarian assignment. Inspired by this setting we observe an interesting connection between our model and the classic proportional multi-winner election problem in social choice.
The conference paper assignment has been studied a number of times over the years in computer science @cite_27 , as has defining and refining notions of fairness for the assignment vectors in multi-agent allocation problems @cite_25 . We build off the work of , who extensively study the notion of fair paper assignments, including lexi-min and rank-maximal assignments, within the context of conference paper assignment. show that for the setting we study, finding an egalitarian optimal assignment and finding a leximin optimal assignment are both NP-hard when there are three or more equivalence classes; and polynomial time computable when there are only two. They also provide an approximation algorithm for leximin optimal assignments. We know that if the capacity constraints are hard values, i.e., each reviewer must review @math papers and each paper must receive exactly @math reviews, then the resulting version of capacitated assignment is NP-hard @cite_3 . Answer set programming for CPAP was studied by ; they encode the CPAP problem in ASP and show that finding a solution that roughly correspond to the leximin optimal and egalitarian solutions can be done in reasonable time for large settings ( @math agents).
@cite_27 @cite_25 @cite_3
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We study the problem of fair allocation for indivisible goods. We use the the maxmin share paradigm introduced by Budish as a measure for fairness. Procacciafirst (EC'14) were first to investigate this fundamental problem in the additive setting. In contrast to what real-world experiments suggest, they show that a maxmin guarantee (1- @math allocation) is not always possible even when the number of agents is limited to 3. While the existence of an approximation solution (e.g. a @math - @math allocation) is quite straightforward, improving the guarantee becomes subtler for larger constants. Procaccia provide a proof for existence of a @math - @math allocation and leave the question open for better guarantees. Our main contribution is an answer to the above question. We improve the result of ! to a @math factor in the additive setting. The main idea for our @math - @math allocation method is clustering the agents. To this end, we introduce three notions and techniques, namely reducibility, matching allocation, and cycle-envy-freeness, and prove the approximation guarantee of our algorithm via non-trivial applications of these techniques. Our analysis involves coloring and double counting arguments that might be of independent interest. One major shortcoming of the current studies on fair allocation is the additivity assumption on the valuations. We alleviate this by extending our results to the case of submodular, fractionally subadditive, and subadditive settings. More precisely, we give constant approximation guarantees for submodular and XOS agents, and a logarithmic approximation for the case of subadditive agents. Furthermore, we complement our results by providing close upper bounds for each class of valuation functions. Finally, we present algorithms to find such allocations for additive, submodular, and XOS settings in polynomial time. Among the tasks to be carried out by conference organizers is the one of assigning reviewers to papers. That problem is known in the literature as the Conference Paper Assignment Problem CPAP. In this paper we approach the solution of a reasonably rich variant of the CPAP by means of Answer Set Programming ASP. ASP is an established logic-based programming paradigm which has been successfully applied for solving complex problems arising in Artificial Intelligence. We show how the CPAP can be elegantly encoded by means of an ASP program, and we analyze the results of an experiment, conducted on real-world data, that outlines the viability of our solution. We present a recommender systems approach to conference paper assignment, i.e., the task of assigning paper submissions to reviewers. We address both the modeling of reviewer-paper preferences (which can be cast as a learning problem) and the optimization of reviewing assignments to satisfy global conference criteria (which can be viewed as constraint satisfaction). Due to the paucity of preference data per reviewer or per paper (relative to other recommender systems applications) we show how we can integrate multiple sources of information to learn reviewer-paper preference models. Our models are evaluated not just in terms of prediction accuracy but in terms of end-assignment quality. Using a linear programming-based assignment optimization, we show how our approach better explores the space of unsupplied assignments to maximize the overall affinities of papers assigned to reviewers. We demonstrate our results on real reviewer bidding data from the IEEE ICDM 2007 conference. 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.