We study the computational problem of computing a fair means clustering of discrete vectors, which admits an equivalent formulation as editing a colored matrix into one with few distinct color-balanced rows by changing at most k values. While NP-hard in both the fairness-oblivious and the fair settings, the problem is well-known to admit a fixed-parameter algorithm in the former "vanilla" setting. As our first contribution, we exclude an analogous algorithm even for highly restricted fair means clustering instances. We then proceed to obtain a full complexity landscape of the problem, and establish tractability results which capture three means of circumventing our obtained lower bound: placing additional constraints on the problem instances, fixed-parameter approximation, or using an alternative parameterization targeting tree-like matrices.
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As the use of AI in society grows, addressing emerging biases is essential to prevent systematic discrimination. Several bias detection methods have been proposed, but, with few exceptions, these tend to ignore transparency. Instead, interpretability and explainability are core requirements for algorithmic fairness, even more so than for other algorithmic solutions, given the human-oriented nature of fairness. We present ABIDE (Argumentative BIas detection by DEbate), a novel framework that structures bias detection transparently as debate, guided by an underlying argument graph as understood in (formal and computational) argumentation. The arguments are about the success chances of groups in local neighbourhoods and the significance of these neighbourhoods. We evaluate ABIDE experimentally and demonstrate its strengths in performance against an argumentative baseline.
Collaborative Representation Learning for Alignment of Tactile, Language, and Vision Modalities
PDF ↗Tactile sensing offers rich and complementary information to vision and language, enabling robots to perceive fine-grained object properties. However, existing tactile sensors lack standardization, leading to redundant features that hinder cross-sensor generalization. Moreover, existing methods fail to fully integrate the intermediate communication among tactile, language, and vision modalities. To address this, we propose TLV-CoRe, a CLIP-based Tactile-Language-Vision Collaborative Representation learning method. TLV-CoRe introduces a Sensor-Aware Modulator to unify tactile features across different sensors and employs tactile-irrelevant decoupled learning to disentangle irrelevant tactile features. Additionally, a Unified Bridging Adapter is introduced to enhance tri-modal interaction within the shared representation space. To fairly evaluate the effectiveness of tactile models, we further propose the RSS evaluation framework, focusing on Robustness, Synergy, and Stability across different methods. Experimental results demonstrate that TLV-CoRe significantly improves sensor-agnostic representation learning and cross-modal alignment, offering a new direction for multimodal tactile representation.
Generative world models have become essential data engines for autonomous driving, yet most focus on videos or occupancy grids and overlook the unique challenges of LiDAR. Extending LiDAR generation to dynamic 4D modeling requires addressing controllability, temporal coherence, and standardized evaluation. We present LiDARCrafter, a unified framework for controllable 4D LiDAR generation and editing. Free-form language instructions are converted into ego-centric scene graphs that guide a tri-branch diffusion model to generate object geometry, motion, and structural priors. An autoregressive module further produces temporally coherent and stable LiDAR sequences with improved global consistency. To enable fair comparison, we introduce a comprehensive benchmark covering scene-, object-, and sequence-level metrics for rigorous and reproducible evaluation. Experiments on nuScenes show that LiDARCrafter achieves state-of-the-art fidelity, controllability, and temporal consistency, paving the way for scalable data augmentation and realistic simulation in diverse scenarios. Code have been publicly available at https://lidarcrafter.github.io.
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.
Centralized Group Equitability and Individual Envy-Freeness in the Allocation of Indivisible Items
PDF ↗We study the fair allocation of indivisible items to groups of agents from the perspectives of both the agents and a centralized allocator. In our setting, the centralized allocator aims to ensure that the allocation is fair both among the groups and between individual agents. This setting applies to many real-world scenarios, such as when a school administrator allocates resources (e.g., office spaces and supplies) to staff members within departments or when a city council allocates limited housing units to families in need across different communities. To ensure fairness between agents, we consider the classical notion of envy-freeness (EF). To ensure fairness among groups, we introduce the notion of centralized group equitability (CGEQ), which captures fairness for groups from the centralized allocator’s perspective. Because an EF or CGEQ allocation does not always exist in general, we consider their natural relaxations: 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 we design efficient algorithms to compute such 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.
Cake-cutting algorithms, which aim to fairly allocate a continuous resource based on individual agent preferences, have seen significant progress over the past two decades. Much of the research has concentrated on fairness, with comparatively less attention given to other important aspects. In 2010, Chen et al. introduced an algorithm that, in addition to ensuring fairness, was strategyproof---meaning agents had no incentive to misreport their valuations. However, even in the absence of strategic incentives to misreport, agents may still hesitate to reveal their true preferences due to privacy concerns (e.g., when allocating advertising time between firms, revealing preferences could inadvertently expose planned marketing strategies or product launch timelines). In this work, we extend the strategyproof algorithm of Chen et al. by introducing a privacy-preserving dimension. To the best of our knowledge, we present the first private cake-cutting protocol, and, in addition, this protocol is also envy-free and strategyproof. Our approach replaces the algorithm’s centralized computation with a novel adaptation of cryptographic techniques, enabling privacy without compromising fairness or strategyproofness. Thus, our protocol encourages agents to report their true preferences not only because they are not incentivized to lie, but also because they are protected from having their preferences exposed.
We study how the design of testing institutions, encompassing both the tests themselves and the procedures used to administer them, shapes selection outcomes in environments with multiple criteria and strategic agents. We model the testing agency as either a set of independent bureaucracies (each test administered separately) or a joint bureaucracy (where test order and personalization can be coordinated). Our mechanism design analysis shows that under a joint bureaucracy, fixed-order sequential mechanisms with stringent tests are optimal for maximizing the probability mass of qualified candidates selected. Furthermore, we demonstrate that personalizing tests through upfront communication, now increasingly feasible via AI and automation, can select all qualified candidates. Finally, we compare institutional settings and quantify the value of controlling test order, showing that the benefit depends critically on the distribution of testees and the stringency of optimal tests. Our results contribute to the design of robust, efficient, and fair testing systems in both human and AI-mediated environments.
Core-selecting combinatorial auctions are popular auction designs that constrain prices to eliminate the incentive for any group of bidders---with the seller---to renegotiate for a better deal. They help overcome the low-revenue issues of classical combinatorial auctions. We introduce a new class of core-selecting combinatorial auctions that leverage bidder information available to the auction designer. We model such information through constraints on the joint type space of the bidders---these are constraints on bidders' private valuations that are known to hold by the auction designer before bids are elicited. First, we show that type space information can overcome the well-known impossibility of incentive-compatible core-selecting combinatorial auctions. We present a revised and generalized version of that impossibility result that depends on how much information is conveyed by the type spaces. We then devise a new family of core-selecting combinatorial auctions and show that they minimize the sum of bidders' incentives to deviate from truthful bidding. We develop new constraint generation techniques---and build upon existing quadratic programming techniques---to compute core prices, and conduct experiments to evaluate the incentive, revenue, fairness, and computational merits of our new auctions. Our new core-selecting auctions directly improve upon existing designs that have been used in many high-stakes auctions around the world. We envision that they will be a useful addition to any auction designer's toolkit.
The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine learning to quantify the individual contribution of features or data points to the performance of a predictive model.Despite its popularity and axiomatic justification, the Shapley value suffers from a computational complexity that scales exponentially with the number of entities involved, and hence requires approximation methods for its reliable estimation. We propose SVAkADD, a novel approximation method that fits a k-additive surrogate game. By taking advantage of k-additivity, we are able to elicit the exact Shapley values of the surrogate game and then use these values as estimates for the original fair division problem. The efficacy of our method is evaluated empirically and compared to competing methods.
This paper bridges two perspectives: it studies the multi-secretary problem through the fairness lens of social choice, and examines multi-winner elections from the viewpoint of online decision making. After identifying the limitations of the prominent proportionality notion of Extended Justified Representation (EJR) in the online domain, the work proposes a set of mechanisms that merge techniques from online algorithms with rules from social choice---such as the Method of Equal Shares and the Nash Rule---and supports them through both theoretical analysis and extensive experimental evaluation.
We consider the problem of assigning items to platforms where each item has a utility associated with each of the platforms to which it can be assigned. Each platform has a soft constraint over the total number of items it serves, modeled via a convex cost function. Additionally, items are partitioned into groups, and each platform also incurs group-specific convex cost over the number of items from each group that can be assigned to the platform. These costs promote group fairness by penalizing imbalances, yielding a soft variation of fairness notions introduced in prior work, such as Restricted Dominance and Minority protection. Restricted Dominance enforces upper bounds on group representation, while Minority protection enforces lower bounds. Our approach replaces such hard constraints with cost-based penalties, allowing more flexible trade-offs. Our model also captures Nash Social Welfare kind of objective. The cost of an assignment is the sum of the values of all the cost functions across all the groups and platforms. The objective is to find an assignment that minimizes the cost while achieving a total utility that is at least a user-specified threshold. The main challenge lies in balancing the overall platform cost with group-specific costs, both governed by convex functions, while meeting the utility constraint. We present an efficient polynomial-time approximation algorithm, supported by theoretical guarantees and experimental evaluation. Our algorithm is based on techniques involving linear programming and network flows. We also provide an exact algorithm for a special case with uniform utilities and establish the hardness of the general problem when the groups can intersect arbitrarily. This work has applications in cloud computing, logistics, resource-constrained machine learning deployment, federated learning, and network design, where resources must be allocated across platforms with diverse cost structures and diminishing returns.
Fair division mechanisms for indivisible goods require agent orderings to deterministically select one allocation when running the algorithm in practice. We introduce position envy-freeness up to one good (PEF1) as a fairness criterion for mechanisms: a mechanism is said to satisfy PEF1 if for any pair of agent orderings, no agent prefers their bundle determined under one ordering to that under another ordering by more than the utility of a single good. First, we propose a scale-invariant, polynomial-time mechanism that satisfies PEF1 and yields an envy-freeness up to one good (EF1) allocation. For the case of two agents, we establish that any mechanism producing a maximum Nash welfare allocation eliminates envy based on positions by removing one good, provided that utilities are positive. Additionally, we present a polynomial-time mechanism based on the adjusted winner procedure, which satisfies PEF1 and produces an EF1 and Pareto optimal allocation for two agents. In contrast, we demonstrate that well-known mechanisms such as round-robin and envy-cycle elimination do not generally satisfy PEF1.
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least advantaged agent at the end of all rounds (optimal) or at the end of every individual round (anytime optimal). We investigate the computational challenges associated with finding (anytime) optimal outcomes and demonstrate that these problems are generally computationally intractable. However, we provide approximation algorithms, fixed-parameter tractable algorithms, and identify several special cases whereby the problem(s) can be solved efficiently. Along the way, we also establish characterizations of Pareto-optimal/maximum matchings, which may be of independent interest to works in matching theory and house allocation.
We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations. As fair we consider the allocations that are envy-free-up-to-any-good (EFX). Finding if EFX allocations always exist, even for agents with additive valuations, is a major open problem in Fair Division. Christodoulou et al. (2023) introduced the (multi-hyper)graph setting, where agents and goods are represented by vertices and edges of a graph, respectively, and only the endpoints of an edge may have non-zero marginal value for it. We show that for hypergraphs with girth at least 4 and agents with general monotone valuations there always exists an EFX allocation and can be constructed in polynomial time. We generalize our approach to also show that multi-hypergraphs with girth (on the simple hypergraph) at least 4 always admit an EFX allocation, as long as there exists a single vertex whose adjacent edges have multiplicity at most the size of that edge minus 2; our construction in this case needs pseudo-polynomial time.
We study the problem of allocating indivisible goods among agents with additive valuation functions to achieve both fairness and efficiency under the constraint that each agent receives exactly the same number of goods (the balanced constraint). While this constraint is common in real-world scenarios such as team drafts or asset division, it significantly complicates the search for allocations that are both fair and efficient. Envy-freeness up to one good (EF1) is a well-established fairness notion for indivisible goods. Pareto optimality (PO) and its stronger variant, fractional Pareto optimality (fPO), are widely accepted efficiency criteria. Our main contribution establishes both the existence and polynomial-time computability of allocations that are simultaneously EF1 and fPO under balanced constraints in two fundamental cases: (1) when agents have at most two distinct types of valuation functions, and (2) when each agent has a personalized bivalued valuation. Our algorithms leverage novel applications of maximum-weight matching in bipartite graphs and duality theory, providing the first polynomial-time solutions for these cases and offering new insights for constrained fair division problems.
We consider the problem of fairly allocating the vertices of a graph among n agents, where the value of a bundle is determined by its cut value---the number of edges with exactly one endpoint in the bundle. This model naturally captures applications such as team formation and network partitioning, where valuations are inherently non-monotonic: the marginal values may be positive, negative, or zero depending on the composition of the bundle. We focus on the fairness notion of envy-freeness up to one item (EF1) and explore its compatibility with several efficiency concepts such as Transfer Stability (TS) that prohibits any transfer of item that benefit one agent at another's expense. For general graphs, our results uncover a non-monotonic relationship between the number of agents n and the existence of allocations satisfying EF1 and transfer stability (TS): such allocations always exist for n=2, may fail to exist for n=3, but exist again for all n>= 4. We further show that existence can be guaranteed for any n by slightly weakening the efficiency requirement or by restricting the graph to forests. All of our positive results are achieved via efficient algorithms.
House allocations concern with matchings involving one-sided preferences, where houses serve as a proxy encoding valuable indivisible resources (e.g. organs, course seats, subsidized public housing units) to be allocated among the agents. Every agent must receive exactly one resource. We study algorithmic approaches towards ensuring fairness in such settings. Minimizing the number of envious agents is known to be computationally hard. We present two tractable approaches to deal with the hardness. When the agents are presented with an initial allocation of houses, we aim to refine this allocation by reallocating a bounded number of houses to reduce the number of envious agents. We show an efficient algorithm when the agents express preference for a bounded number of houses and houses are accepted by a bounded number of agents. Next, we consider single peaked preference domain and present a polynomial time algorithm for finding an allocation that minimize the number of envious agents. We further extend it to satisfy Pareto efficiency. Our former algorithm works for other measures of envy such as total envy, or maximum envy, with suitable modifications. Finally, we present an empirical analysis recording the fairness-welfare trade-off of our algorithms.
This paper studies the problem of minimizing group-level inequity in facility location games on the real line, where agents belong to different groups and may act strategically. We explore a fairness-oriented objective that minimizes the maximum group effect. For each group, the group effect is defined as its total or maximum distance to the nearest facility, weighted by group-specific factors. We show that this formulation generalizes several prominent optimization objectives, including the classical utilitarian (social cost) and egalitarian (maximum cost) objectives, as well as two group-fair objectives, maximum total and average group cost. In order to minimize the maximum group effect, we first propose two novel mechanisms for the single-facility case, the Balanced mechanism and the Major-Phantom mechanism. Both are strategyproof and achieve tight approximation guarantees under distinct formulations of the maximum group effect objective. Our mechanisms not only close the existing gap in approximation bounds for the group-fairness objectives, maximum total group cost and maximum average group cost, but also unify many classical truthful mechanisms within a broader fairness-aware framework. For the two-facility case, we revisit and extend the classical endpoint mechanism to our generalized setting and demonstrate that it provides tight bounds for two distinct maximum group effect objectives.
Diffusion auction design is a new trend in mechanism design which extends the original incentive compatibility property to include buyers' private connection report. Reporting connections is equivalent to inviting their neighbors to join the auction in practice. Then, the social welfare is collectively accumulated by all participants: reporting high valuations or inviting high-valuation neighbors. Hence, we can measure each participant's contribution by the marginal social welfare increase due to her participation. Therefore, in this paper, we introduce a new property called Shapley fairness to capture participants' social welfare contribution and use it as a benchmark to guide our auction design for a fairer utility allocation. Not surprisingly, none of the existing diffusion auctions has ever approximated the fairness, because Shapley fairness depends on each buyer's own valuation and this dependence can easily violate incentive compatibility. Thus, we combat this challenge by proposing a new diffusion auction called Permutation Diffusion Auction (PDA) for selling k homogeneous items, which is the first diffusion auction satisfying 1/(k+1)-Shapley fairness, incentive compatibility and individual rationality. Moreover, PDA can be extended to the general combinatorial auction setting where the literature did not discover meaningful diffusion auctions yet.