arXiv subjects

Tianze Wei

Publications and source records attributed to Tianze Wei.

6 recordsLinked to original sources

arXiv2025

Centralized Group Equitability and Individual Envy-Freeness in the Allocation of Indivisible Items

We study the fair allocation of indivisible items for groups of agents from the perspectives of the agents and a centralized allocator. In our setting, the centralized allocator is interested in ensuring the allocation is fair among the groups and between agents. This setting applies to many real-world scenarios, including when a school administrator wants to allocate resources (e.g., office spaces and supplies) to staff members in departments and when a city council allocates limited housing units to various families in need across different communities. To ensure fair allocation between agents, we consider the classical envy-freeness (EF) notion. To ensure fairness among the groups, we define the notion of centralized group equitability (CGEQ) to capture the fairness for the groups from the allocator's perspective. Because an EF or CGEQ allocation does not always exist in general, we consider their corresponding natural relaxations of envy-freeness to one item (EF1) and centralized group equitability up to one item (CGEQ1). For different classes of valuation functions of the agents and the centralized allocator, we show that allocations satisfying both EF1 and CGEQ1 always exist and design efficient algorithms to compute these allocations. We also consider the centralized group maximin share (CGMMS) from the centralized allocator's perspective as a group-level fairness objective with EF1 for agents and present several results.

cs.GT↗

arXiv2025

Achieving Equitability with Subsidy

We study the fair allocation problem of indivisible items with subsidy. In this paper, we focus on the notion of fairness - equitability (EQ), which requires that items be allocated such that all agents value the bundle they receive equally. First, we study the upper bounds of the minimum required subsidy to achieve EQ in different item settings and provide the corresponding lower bounds. Second, we consider the bounded subsidy for achieving EQ and another popular notion of fairness - envy-freeness (EF), and give a characterization of allocations that can achieve both EQ and EF. Finally, we analyze the bounds of subsidy of allocations achieving fairness and efficiency (utilitarian social welfare or Nash welfare) and design several polynomial-time algorithms to compute the desired allocation.

cs.GT↗

arXiv2025

Online Fair Allocations with Binary Valuations and Beyond

In an online fair allocation problem, a sequence of indivisible items arrives online and needs to be allocated to offline agents immediately and irrevocably. In our paper, we study the online allocation of either goods or chores. We employ popular fairness notions, including envy-freeness up to one item (EF1) and maximin share fairness (MMS) to capture fairness, and utilitarian social welfare (USW) to measure efficiency. For both settings of items, we present a series of positive results regarding the existence of fair and efficient allocations with widely studied classes of additive binary and personalized bi-valued valuation/cost functions. Furthermore, we complement our results by constructing counterexamples to establish our results as among the best guarantees possible.

cs.GT↗

arXiv2025

A Complete Landscape of EFX Allocations on Graphs: Goods, Chores and Mixed Manna

We study envy-free up to any item (EFX) allocations on simple graphs where vertices and edges represent agents and items respectively. An agent (vertex) is only interested in items (edges) that are incident to her and all other items always have zero marginal value to her. Christodoulou et al. [EC, 2023] first proposed this setting and studied the case of goods where every item has non-negative marginal values to every agent. In this work, we significantly generalize this setting and provide a complete set of results by considering the allocation of arbitrary items that can be goods, chores, or mixed manna under doubly monotone valuations with a mild assumption. For goods, we complement the results by Christodoulou et al. [EC, 2023] by considering another weaker notion of EFX in the literature and showing that an orientation -- a special allocation where each edge must be allocated to one of its endpoint agents -- that satisfies the weaker notion always exists and can be computed in polynomial time, contrary to the stronger notion for which an orientation may not exist and determining its existence is NP-complete. For chores, we show that an envy-free allocation always exists, and an EFX orientation may not exist but its existence can be determined in polynomial time. For mixed manna, we consider the four notions of EFX in the literature. We prove that an allocation that satisfies the strongest notion of EFX may not exist and determining its existence is NP-complete, while one that satisfies any of the other three notions always exists and can be computed in polynomial time. We also prove that an orientation that satisfies any of the four notions may not exist and determining its existence is NP-complete.

cs.GT↗

arXiv2023

Maximin-Aware Allocations of Indivisible Chores with Symmetric and Asymmetric Agents

The real-world deployment of fair allocation algorithms usually involves a heterogeneous population of users, which makes it challenging for the users to get complete knowledge of the allocation except for their own bundles. Chan et al. [IJCAI 2019] proposed a new fairness notion, maximin-awareness (MMA), which guarantees that every agent is not the worst-off one, no matter how the items that are not allocated to her are distributed. We adapt and generalize this notion to the case of indivisible chores and when the agents may have arbitrary weights. Due to the inherent difficulty of MMA, we also consider its up to one and up to any relaxations. A string of results on the existence and computation of MMA related fair allocations, and their connections to existing fairness concepts is given.

cs.GT↗

arXiv2023

Online Nash Welfare Maximization Without Predictions

The maximization of Nash welfare, which equals the geometric mean of agents' utilities, is widely studied because it balances efficiency and fairness in resource allocation problems. Banerjee, Gkatzelis, Gorokh, and Jin (2022) recently introduced the model of online Nash welfare maximization for $T$ divisible items and $N$ agents with additive utilities with predictions of each agent's utility for receiving all items. They gave online algorithms whose competitive ratios are logarithmic. We initiate the study of online Nash welfare maximization \emph{without predictions}, assuming either that the agents' utilities for receiving all items differ by a bounded ratio, or that their utilities for the Nash welfare maximizing allocation differ by a bounded ratio. We design online algorithms whose competitive ratios only depend on the logarithms of the aforementioned ratios of agents' utilities and the number of agents.

cs.DS↗