We consider a setting where goods are allocated to agents by way of an allocation platform (e.g., a matching platform). An “allocation facilitator” aims to increase the overall utility/social-good of the allocation by encouraging (some of the) agents to relax (some of) their restrictions. At the same time, the advice must not hurt agents who would otherwise be better off. Additionally, the facilitator may be constrained by a “bound” (a.k.a. `budget'), limiting the number and/or type of restrictions it may seek to relax. We consider the facilitator's optimization problem of choosing an optimal set of restrictions to request to relax under the aforementioned constraints. Our contributions are three-fold: (i) We provide a formal definition of the problem, including the participation guarantees to which the facilitator should adhere. We define a hierarchy of participation guarantees and also consider several social-good functions. (ii) We provide polynomial algorithms for solving various versions of the associated optimization problems, including one-to-one and many-to-one allocation settings. (iii) We demonstrate the benefits of such facilitation and relaxation, and the implications of the different participation guarantees, using extensive experimentation on three real-world datasets.

Optimal allocation of agricultural water in the event of droughts is an important global problem. In addressing this problem, many aspects, including the welfare of farmers, the economy, and the environment, must be considered. Under this backdrop, our work focuses on several resource-matching problems accounting for agents with multi-crop portfolios, geographic constraints, and fairness. First, we address a matching problem where the goal is to maximize a welfare function in two-sided markets where buyers' requirements and sellers' supplies are represented by value functions that assign prices (or costs) to specified volumes of water. For the setting where the value functions satisfy certain monotonicity properties, we present an efficient algorithm that maximizes a social welfare function. When there are minimum water requirement constraints, we present a randomized algorithm which ensures that the constraints are satisfied in expectation. For a single seller--multiple buyers setting with fairness constraints, we design an efficient algorithm that maximizes the minimum level of satisfaction of any buyer. We also present computational complexity results that highlight the limits on the generalizability of our results. We evaluate the algorithms developed in our work with experiments on both real-world and synthetic data sets with respect to drought severity, value functions, and seniority of agents.

In many settings, there is an organizer who would like to divide a set of agents into $k$ coalitions, and cares about the friendships within each coalition. Specifically, the organizer might want to maximize utilitarian social welfare, maximize egalitarian social welfare, or simply guarantee that every agent will have at least one friend within his coalition. However, in many situations, the organizer is not familiar with the friendship connections, and he needs to obtain them from the agents. In this setting, a manipulative agent may falsely report friendship connections in order to increase his utility. In this paper, we analyze the complexity of finding manipulation in such $k$-coalitional games on graphs. We also introduce a new type of manipulation, socially-aware manipulation, in which the manipulator would like to increase his utility without decreasing the social welfare. We then study the complexity of finding socially-aware manipulation in our setting. Finally, we examine the frequency of socially-aware manipulation and the running time of our algorithms via simulation results.

In many allocation problems, understanding individual agents' needs, wants, and tradeoffs is crucial for providing fair and efficient solutions. This paper begins with motivating applications and critical definitions. We review existing results, such as advising agents on relaxing restrictions for improved resource allocation, optimizing task allocation in online settings without rejection of a task, and more. We conclude by outlining three potential directions for future research.

Assigning tasks to service providers is a frequent procedure across various applications. Often the tasks arrive dynamically while the service providers remain static. Preventing task rejection caused by service provider overload is of utmost significance. To ensure a positive experience in relevant applications for both service providers and tasks, fairness must be considered. To address the issue, we model the problem as an online matching within a bipartite graph and tackle two minimax problems: one focuses on minimizing the highest waiting time of a task, while the other aims to minimize the highest workload of a service provider. We show that the second problem can be expressed as a linear program and thus solved efficiently while maintaining a reasonable approximation to the objective of the first problem. We developed novel methods that utilize the two minimax problems. We conducted extensive simulation experiments using real data and demonstrated that our novel heuristics, based on the linear program, performed remarkably well.

Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which they want to be matched. Viewing such an application as a multi-round matching problem on a bipartite compatibility graph between agents and resources, we show that a solution (i.e., a set of matchings, with one matching per round) can be found efficiently if one exists. To cope with situations where a solution does not exist, we consider two extensions. In the first extension, a benefit function is defined for each agent and the objective is to find a multi-round matching to maximize the total benefit. For a general class of benefit functions satisfying certain properties (including diminishing returns), we show that this multi-round matching problem is efficiently solvable. This class includes utilitarian and Rawlsian welfare functions. For another benefit function, we show that the maximization problem is NP-hard. In the second extension, the objective is to generate advice to each agent (i.e., a subset of requirements to be relaxed) subject to a budget constraint so that the agent can be matched. We show that this budget-constrained advice generation problem is NP-hard. For this problem, we develop an integer linear programming formulation as well as a heuristic based on local search. We experimentally evaluate our algorithms on synthetic networks and apply them to two real-world situations: shared office spaces and matching courses to classrooms.

Many applications where tasks should be assigned to agents can be modeled as matching in bipartite graphs. In this paper, we consider applications where tasks arrive dynamically and rejection of a task may have significant adverse effects on the requester, therefore performing the task with some delay is preferred over complete rejection. The performance time of a task depends on the task, the agent, and the assignment, and only its distribution is known in advance. The actual time is known only after the task performance when the agent is available for a new assignment. We consider such applications to be one of two arrival types. With the first type, the arrival distribution is known in advance, while there is no assumption about the arrival times and order with the second type. For the first type, we present an LP-based online algorithm with a competitive ratio of 0 . 5. For the second type, we show no online algorithm with a constant competitive ratio. We run extensive experiments to evaluate our algorithm in a real-world dataset, demonstrating the advantages of the LP approach.

Teleoperation of autonomous vehicles has been gaining a lot of attention recently and is expected to play an important role in helping autonomous vehicles handle difficult situations which they cannot handle on their own. In such cases, a remote driver located in a teleoperation center can remotely drive the vehicle until the situation is resolved. However, teledriving is a challenging task and requires many cognitive resources from the teleoperator. Our goal is to assist the remote driver in some complex situations by giving the driver appropriate advice. The advice is displayed on the driver’s screen to help her make the right decision. To this end, we introduce the TeleOperator Advisor (TOA), an adaptive agent that provides assisting advice to a remote driver. We evaluate the TOA in a simulation-based setting in two scenarios: overtaking a slow vehicle and passing through a traffic light. Results indicate that our advice helps to reduce the cognitive load of the remote driver and improve driving performance.

Many applications involving the allocation of resources or tasks can be modeled as matching problems in bipartite graphs. In many of these applications, allocation is performed multiple times. An example is the allocation of classrooms to course instructors, which is done every semester. To improve their chances of being assigned, instructors may relax some of their restrictions. Another example is course and classroom assignments made for weekly workdays. In this case, however, the assignment is made multiple times at once (once for each workday of the week). Finally, in task assignment problems where resources are reusable, each resource can be assigned multiple times. We describe algorithmic solutions to some of these problems and demonstrate their effectiveness in applications such as car teleoperation, desk sharing, and classroom assignment. Finally, we discuss several directions and ideas for extending our work and solving other relevant problems.

Many scenarios where agents with restrictions compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have restrictions that make them incompatible with some resources. We assume that a Principal chooses a maximum matching randomly so that each agent is matched to a resource with some probability. Agents would like to improve their chances of being matched by modifying their restrictions within certain limits. The Principal’s goal is to advise an unsatisfied agent to relax its restrictions so that the total cost of relaxation is within a budget (chosen by the agent) and the increase in the probability of being assigned a resource is maximized. We establish hardness results for some variants of this budget-constrained maximization problem and present algorithmic results for other variants. We experimentally evaluate our methods on synthetic datasets as well as on two novel real-world datasets: a vacation activities dataset and a classrooms dataset.

Many scenarios where agents with preferences compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have preferences that make them incompatible with some resources. We assume that a Principal chooses a maximum matching randomly so that each agent is matched to a resource with some probability. Agents would like to improve their chances of being matched by modifying their preferences within certain limits. The Principal's goal is to advise an unsatisfied agent to relax its restrictions so that the total cost of relaxation is within a budget (chosen by the agent) and the increase in the probability of being assigned a resource is maximized. We develop efficient algorithms for some variants of this budget-constrained maximization problem and establish hardness results for other variants. For the latter variants, we also develop algorithms with performance guarantees. We experimentally evaluate our methods on synthetic datasets as well as on two novel real-world datasets: a vacation activities dataset and a classrooms dataset.

Let P be a set of 2n points in the plane, and let MC (resp., MNC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing MNC. We first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)⩽210⋅bn(MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(MNC)/bn(MC)⩽210. Finally, we show that when the points of P are in convex position, one can compute MNC in O(n3) time, improving a result in [7].