| Author: | Sifat, Md.habibur Rahman |
| Title: | Algorithmic solutions for maximin share allocation under budget feasible constraints |
| Advisors: | Li, Bo (COMP) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Subject: | Resource allocation -- Mathematical models Assignment problems (Programming) -- Mathematical models Computer algorithms -- Mathematical models Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Computing |
| Pages: | x, 113 pages : color illustrations |
| Language: | English |
| Abstract: | Fair division is an important research field in multi-agent systems that integrates computer science and social science. A traditional fair division problem is often modeled as allocating a set of resources to a set of agents, where each agent’s absolute value depends on her own allocated resources, but her relative happiness depends on the comparison of her due share with others. Fairness is mostly captured by envy-freeness and proportionality in the literature. Although an exact envy-free or proportional allocation always exists when resources are divisible (such as funding and land), it merely exists when resources are indivisible (such as equipment and labor). Accordingly, for indivisible resources, an extensively studied subject is investigating to what extent the relaxations of these fairness notions can be satisfied by either designing (approximation) algorithms or identifying tricky instances to show the inherent difficulties of the problem, so that no algorithm can be better than a certain performance. This thesis aims to expand the theory of algorithmic fair division by considering combinatorial constraints over agents and items with theoretical and experimental studies. Despite rapid progress in fair division, problems under practical constraints remain largely unexplored. In real-world scenarios, however, agents’ satisfaction with the final allocation depends not only on items’ generic value but also on the constraints induced by items' essential properties, which form the basis of agents' reasoning and largely affect the whole system's structure and performance. For example, items may actually have prices or physical sizes, and agents have budgets or capacities to support the assigned items accordingly, in which situation the constraints can be abstracted as knapsacks. There are also more complicated situations when the items' properties cannot be described by a single parameter, such as job scheduling constraints and incentive-compatible constraints. In this thesis, we will first characterize proper fairness notions for combinatorial constrained settings and then investigate to what extent fairness can be guaranteed by designing algorithms and analyzing the limits of algorithms. Further, we study budget feasible constraints within the hereditary set system, where resources have values and sizes, and agents face budget limitations on the total resource size they can acquire. A feasible allocation must ensure that the size of the allocated bundle to each agent remains within their budget limit. Our analysis reveals that Li and Vetta's [TEAC, 2021] algorithm fails to maintain a 0.371 approximation ratio for this problem. To address this, we propose a novel algorithm that improves the approximation ratio to 12/31 ≈ 0.387. Further, we showed experimental studies to show that our proposed algorithm ensures considerably more utilities than 12/31 and outperformed Li and Vetta's algorithm for all instances. After that, we extended our study to generalized assignment constraints. This is a generalized setting of budget constraints, where item sizes are not identical. We showed that MMS allocation does not exist under generalized assignment constraints even for two agents' instances, and we guaranteed 2/3-MMS allocation for this scenario. For the arbitrary number of agents, we improved the lower bound to 4/15 ≈ 26666667. |
| Rights: | All rights reserved |
| Access: | open access |
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