In this paper, we study the heterogeneous facility location game with fractional preferences under resource constraints. In this model, a group of agents are positioned along the interval [0, 1], where each agent has position information and fractional preferences indicated as support weights for facilities. Our main focus is to design mechanisms that choose and locate one facility out of two facilities while motivating agents to truthfully report their information, aiming to approximately maximize the social utility, defined as the sum of utilities of all agents. Based on the types of private information held by agents, we consider three different settings. For the known-preferences setting, we provide a deterministic group strategy-proof mechanism with 2-approximation and a randomized group strategy-proof mechanism with 4/3 -approximation. We also provide lower bounds of 2 on the approximation ratio for any deterministic strategy-proof mechanism and 1.043 for any randomized strategy-proof mechanism. For the known-positions setting and the general setting, we present a deterministic group strategy-proof mechanism with 6-approximation and a randomized strategy-proof mechanism with 4-approximation, respectively. Furthermore, we give lower bounds of 1.554 for any deterministic strategy-proof mechanism and 1.2 for any randomized strategy-proof mechanism in the known-positions setting. Finally, we extend the model to the scenario of choosing k facilities out of m facilities. For the known-preferences setting, we provide a 2-approximate deterministic group strategy-proof mechanism, which is also the best deterministic strategy-proof mechanism. For the known-positions setting, when k ≥ 2 , we give a lower bound of 2-1/k for any deterministic strategy-proof mechanism.

This paper investigates the problem of shared resource allocation, where a set of agents must be assigned to heterogeneous resources, with each agent allocated exactly one resource and each resource potentially shared by multiple agents. An agent’s utility for a given resource is jointly determined by the resource's type and the number of agents sharing it. We focus on two fundamental classes of monotone valuations: monotone nondecreasing and monotone nonincreasing, where an agent’s utility respectively increases or decreases with the number of agents sharing the resource. Within this shared resource framework, we examine classical notions of fairness and stability, including maximin-share fairness, envy-freeness, Nash stability, and two epistemic relaxations—epistemic envy-freeness and epistemic Nash stability—as well as swap stability. We propose formal definitions adapted to this setting and systematically analyze the relationships among these concepts. The primary contributions of this work consist of establishing existence and computational complexity results for each notion under both monotonicity assumptions and developing polynomial-time algorithms in cases where fair or stable allocations are guaranteed to exist.

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.

This paper investigates temporal fair division, a setting where items are allocated over multiple rounds and agents require cumulative fairness over time. We focus on dynamic extensions of classic fairness notions: Temporal Envy-Freeness Up to Any Good (TEFX), its α-TEFX approximation, and Temporal Maximin Share (TMMS). Because these strict fairness criteria are known to be generally impossible to satisfy, we analyze the model under constraints to map the boundary between what is possible and what is not. Our contribution systematically maps the structural boundaries of these temporal fairness notions. Our main technical result introduces a novel dynamic backtracking framework that achieves exact TEFX for Strong Binary Valuations. We prove, via a lexicographical potential function argument, that this bounded historical reallocation systematically resolves temporal envy cycles and terminates in finite time. Finally, we establish tight approximation ratios for α-TEFX under identical valuations and bi-valued goods, alongside targeted impossibility results for TEFX and TMMS, demonstrating exactly where temporal fairness is mathematically unattainable, and properly contextualizing prior algorithms that only implicitly satisfied our newly defined TMMS metric.

We study temporal fair division, where agents receive goods over multiple rounds and cumulative fairness is required. We investigate Temporal Envy-Freeness Up to One Good (TEF1) and Up to Any Good (TEFX), its approximation α-TEFX, and Temporal Maximin Share (TMMS). Motivated by known impossibilities in standard settings, we consider the model in various restricted settings and extend it by introducing scheduling. Our main contributions draw the boundary between possibility and impossibility. First, regarding temporal fair division without scheduling, we prove that while constant-factor α-TEFX is impossible in general, a 1/2-approximation is achievable for generalized binary valuations and identical days with two agents. Second, regarding temporal fair division with scheduling, we demonstrate that a scheduling buffer of size at least n/2 enables TEF1 for identical days. However, we establish that TEFX and TMMS remain largely impossible even with scheduling or restricted domains. These results highlight the inherent difficulty of strict temporal fairness and quantify the trade-offs required to achieve approximation guarantees.

Urban Network Security Games (UNSGs), which model the strategic allocation of limited security resources on city road networks, are critical for urban safety. However, finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and combinatorial action spaces. One common approach to addressing these games is the Policy-Space Response Oracle (PSRO) framework, which requires computing best responses (BR) at each iteration. However, precisely computing exact BRs is impractical in large-scale games, and employing reinforcement learning to approximate BRs inevitably introduces errors that limit the overall effectiveness of the PSRO methods. Recent advancements in leveraging non-convex stochastic optimization to approximate an NE offer a promising alternative to the burdensome BR computation. However, utilizing existing stochastic optimization techniques with an unbiased loss function for UNSGs remains challenging because the action spaces are too vast to be effectively represented by neural networks. To address these issues, we introduce Tree-based Stochastic Optimization (TSO), a framework that bridges the gap between the stochastic optimization paradigm for NE-finding and the demands of UNSGs. Specifically, we employ the tree-based action representation that maps the whole action space onto a tree structure, addressing the challenge faced by neural networks in representing actions when the action space cannot be enumerated. We then incorporate this representation into the loss function and theoretically demonstrate its equivalence to the unbiased loss function. To further enhance the quality of the converged solution, we introduce a sample-and-prune mechanism that reduces the risk of being trapped in suboptimal local optima. Extensive experimental results indicate the superiority of TSO over other baseline algorithms in addressing the UNSGs.

The house allocation problem is a classical one-sided matching problem that concerns the assignment of a set of m houses to n agents according to their preferences, where each agent is assigned exactly one house. Among the various objectives studied in this setting, envy-freeness is one of the most widely adopted fairness criteria. As envy-free house allocations do not always exist, we address this challenge by introducing subsidies and aim to compute allocations that achieve envy-freeness with minimum total subsidy. For binary instances, we show that a total subsidy of at most (n-1) suffices to guarantee envy-freeness in house allocation, and this bound is tight. Building on the known NP-hardness for general utilities, we further show that computing an allocation that minimizes the total subsidy is NP-hard, even under binary utilities. However, when there are only a bounded number of types of agents with binary utilities, the problem can be solved in polynomial time. Finally, we present a polynomial time algorithm that computes the minimum subsidy required to achieve envy-freeness for two types of agents with general utilities.

We study temporal fair division of indivisible mixed manna. Items arrive over time and must be allocated irrevocably; an item may be a good for some agents, a chore for others, and neutral for the rest. We require the cumulative allocation after every round to be envy-free up to one item (TEF1). Although deciding whether a TEF1 allocation exists is NP-hard even for goods, we identify several tractable settings. First, with at most k item types, an online cyclic rule guarantees EF⌈ k/2⌉ after every item arrival. Thus, every instance with at most two types admits an online TEF1 allocation; moreover, when the numbers of agents and types are fixed, TEF1 existence can be decided in polynomial time. Second, under agreement after agent-specific scaling, provided that the scaling factors are known before arrivals begin, an online rule produces an allocation that is EF1 and Pareto optimal after every item arrival. Third, for a two-part arrival sequence with common rankings, we give a rule that is EF1 after every item arrival. Fourth, when the number of agents is fixed and values are bounded integers, we give an exact pseudo-polynomial algorithm for deciding TEF1 existence. Finally, for goods, every TEF1 allocation gives each agent at least 1/n of her maximin share after every round; this factor is tight even for identical valuations and two rounds. Deciding whether an exact temporal maximin-share allocation exists is NP-hard for both goods and chores, even with identical valuations, two agents, and two rounds.

Deep learning models often struggle with distribution shifts between training and deployment environments. Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, which is called as the \emph{uncertainty set}. However, the efficacy of DRO heavily depends on the design of uncertainty set, and existing methods often perform suboptimally due to inappropriate and inflexible uncertainty sets. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: \emph{semantic calibration}, which bootstraps semantically meaningful transport costs via inverse OT, and \emph{adaptive refinement}, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis on this adaptive process and prove the theoretical convergence guarantee. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-of-the-art robustness.

Mobile crowdsourcing has emerged as a popular approach for organizations to leverage the collective intelligence of a crowd of users to obtain services. Considering users' costs for providing services, it is vital for the requester to design incentive mechanisms to encourage users' participation in crowdsourcing under the budget constraint. This aligns with the concept of budget-feasible mechanism design. Existing budget-feasible mechanisms often assume immediate user reachability and willingness of joining the crowdsourcing, which is unrealistic. To address this issue, a promising approach is to have participating users diffuse auction information to potential users in the social network. However, this brings another challenge in that participating users can be strategic and therefore hesitant to invite more potential competitors to join the crowdsourcing platform. In this paper, we focus on developing diffusion mechanisms that incentivize strategic users to actively diffuse auction information through the social network. This helps to attract more informed users and ultimately increases the value of the procured services. Specifically, we propose optimal budget-feasible diffusion mechanisms that simultaneously guarantee individual rationality, budget-feasibility, strong budget-balance, incentive-compatibility (i.e., users report real costs and diffuse auction information to all their neighbors) and approximation. Experiment results under real datasets further demonstrate the efficiency of proposed mechanisms.

The main result of this paper is an almost approximation-preserving polynomial-time reduction from the most general multi-parameter Bayesian contract design (BCD) to single-parameter BCD. That is, for any multi-parameter BCD instance $I^M$, we construct a single-parameter instance $I^S$ such that any $\beta$-approximate contract (resp. menu of contracts) of $I^S$ can in turn be converted to a $(\beta -\epsilon)$-approximate contract (resp. menu of contracts) of $I^M$. The reduction is in time polynomial in the input size and $\log(\frac{1}{\epsilon})$; moreover, when $\beta = 1$ (i.e., the given single-parameter solution is exactly optimal), the dependence on $\frac{1}{\epsilon}$ can be removed, leading to a polynomial-time exact reduction. This efficient reduction is somewhat surprising because in the closely related problem of Bayesian mechanism design, a polynomial-time reduction from multi-parameter to single-parameter setting is believed to not exist. Our result demonstrates the intrinsic difficulty of addressing moral hazard in Bayesian contract design, regardless of being single-parameter or multi-parameter. As byproducts, our reduction answers two open questions in recent literature of algorithmic contract design: (a) it implies that optimal contract design in single-parameter BCD is not in APX unless P=NP even when the agent's type distribution is regular, answering the open question of [Alon et al. 2021] in the negative; (b) it implies that the principal's (order-wise) tight utility gap between using a menu of contracts and a single contract is $\Theta(n)$ where $n$ is the number of actions, answering the major open question of [Guruganesh et al. 2021] for the single-parameter case.

We consider a general non-stochastic online pricing bandit setting in a procurement scenario where a buyer with a budget wants to procure items from a fixed set of sellers to maximize the buyer's reward by dynamically offering purchasing prices to the sellers, where the sellers' costs and values at each time period can change arbitrarily and the sellers determine whether to accept the offered prices to sell the items. This setting models online pricing scenarios of procuring resources or services in multi-agent systems. We first consider the offline setting when sellers' costs and values are known in advance and investigate the best fixed-price policy in hindsight. We show that it has a tight approximation guarantee with respect to the offline optimal solutions. In the general online setting, we propose an online pricing policy, Granularity-based Pricing (GAP), which exploits underlying side-information from the feedback graph when the budget is given as the input. We show that GAP achieves an upper bound of O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln B) on the alpha-regret where n, v_{max}, c_{min}, and B are the number, the maximum value, the minimum cost of sellers, and the budget, respectively. We then extend it to the unknown budget case by developing a variant of GAP, namely Doubling-GAP, and show its alpha-regret is at most O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln2 B). We also provide an alpha-regret lower bound Omega(v_{max}sqrt{Bn/c_{min}}) of any online policy that is tight up to sub-linear terms. We conduct simulation experiments to show that the proposed policy outperforms the baseline algorithms.

In this paper, we study a fair resource scheduling problem involving the assignment of a set of interval jobs among a group of heterogeneous machines. Each job is associated with a release time, a deadline, and a processing time. A machine can process a job if the entire processing period falls within the release time and deadline of the job. Each machine can process at most one job at any given time, and different jobs yield different utilities for the machines. The goal is to find a fair and efficient schedule of the jobs. We discuss the compatibility between envy-freeness up to any item (EFX) and various efficiency concepts. Additionally, we present polynomial-time algorithms for various settings.

We consider the k-facility location problems with capacity constraints in bounded location space from the mechanism design perspective. In this problem, we seek to locate k capacity constrained facilities in a bounded interval (i.e., B = [b(l), b(r)]) to serve agents, who have preferences on the ideal locations of the facilities in the interval. Our goal is to design strategyproof mechanisms to elicit agents' true ideal locations and locate facilities that minimize the social cost and maximum cost, which are defined to be the sum and the maximum of the agents' costs (i.e., agents' distances to their facilities), respectively. For the equal capacity setting without spare capacity (i.e., all the agents can be served exactly), we provide a deterministic strategyproof mechanism. For any bounded interval (i.e., b(l), b(r) is an element of R), our mechanism has approximation ratios of n - 1 for the social cost and 4 for the maximum cost with k >= 3 facilities and n >= 3 agents. We also establish lower bounds of n 2 for the social cost by a common class of deterministic mechanisms that order agents from left to right, and 2 for the maximum cost by any deterministic mechanism. Our mechanism also achieves tight bounds for both costs with k < 3 facilities. We then consider the equal capacity setting with spare capacity and the arbitrary capacity setting without spare capacity. For these two settings and any bounded interval, we provide randomized strategyproof mechanisms with approximation ratios of n/2 for the social cost and 2 for the maximum cost with any number of facilities. We complement this result by establishing lower bounds of 5/3 for the social cost and 3/2 for the maximum cost.

We study facility location games with externalities where agents are located on a real line and divided into groups. The cost of an agent is affected by the facility location and their group members. The goal is to design mechanisms to locate a facility to approximately optimize group-fair objectives while eliciting the agents' locations truthfully. We consider two types of group interactions: competitive and collaborative, and two group-fair objectives, minimizing the maximum total group cost and minimizing the maximum average group cost. For each scenario, we analyze classic mechanisms, presenting their approximation ratios, and introduce new mechanisms that achieve improved approximation ratios. Additionally, we establish tight lower bounds for each setting, demonstrating that our mechanisms are the best possible.

We study the k-facility location games with optional preferences on the line. In the games, each strategic agent has a public location preference on the k facility locations and a private optional preference on the preferred/acceptable set of facilities out of the k facilities. Our goal is to design strategyproof mechanisms to elicit agents’ optional preferences and locate k facilities to minimize the social or maximum cost of agents based on their facility preferences and public agent locations. We consider two variants of the facility location games with optional preferences: the Min variant and the Max variant where the agent’s cost is defined as their distance to the closest acceptable facility and the farthest acceptable facility, respectively. For the Min variant, we present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost with k ≥ 3 facilities, achieving approximation ratios of 3 and 2n+1 respectively. We complement the results by establishing lower bounds of 3/2 and n/4 for the approximation ratios achievable by any deterministic strategyproof mechanisms for the maximum cost and social cost, respectively. We then improve our results in a special setting of the Min variant where there are exactly three facilities and present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost. For the Max variant, we present an optimal deterministic strategyproof mechanism for the maximum cost and a k-approximation deterministic strategyproof mechanism for the social cost.

This paper studies a scheduling problem with machine calibrations for multi-interval jobs. More exactly, there are n (possibly weighted) jobs of unit size that must be scheduled on a single initially uncalibrated machine. The machine can process jobs only when calibrated, and such a calibration lasts for T time slots. The standard model by Bender et al. [Bender MA, Bunde DP, Leung VJ, McCauley S, Phillips CA (2013) Efficient scheduling to minimize calibrations. Blelloch GE, Vöcking B, eds. 25th ACM Sympos. Parallelism Algorithms Architectures SPAA ‘13 (ACM, New York), 280–287] assumes that each job has a release time and deadline between which it must be processed. We study a generalization in which each job must be processed during one of possibly many job-dependent time intervals. We consider two objectives: In the minimization version, our goal is to minimize the number of calibrations while scheduling all jobs. In the maximization version, our goal is to maximize the total weight of scheduled jobs while using at most B calibrations. For the minimization version, we present a logarithmic approximation algorithm. We also prove that the problem is set-cover hard, implying that our algorithm is optimal up to a constant factor unless P = NP. The special case when each job may be scheduled in at most two time slots is shown to be vertex-cover hard, implying that there is no [Formula: see text]-approximation algorithm based on the unique game conjecture. For the maximization version, we give an algorithm with approximation ratio [Formula: see text]. This improves upon the previously best-known algorithm, which has an approximation ratio of 1/3 [Chau V, Feng S, Li M, Wang Y, Zhang G, Zhang Y (2019) Weighted throughput maximization with calibrations. Friggstad Z, Sack JR, Salavatipour MR, eds. Algorithms Data Structures 16th Internat. Sympos. WADS 2019 Proc., Lecture Notes in Computer Science, vol. 11646 (Springer, New York), 311–324]. Moreover, we also prove that our bound on the approximation ratio is tight. Although all hardness results mentioned above hold for any [Formula: see text], we provide optimal polynomial-time algorithms for T = 2 in both the minimization version and the maximization version. Finally, we show that our methods can be extended into the m identical machines case by losing some running time, whereas all algorithmic results remain the same in both versions. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.0430 .

Federated learning (FL) is a promising approach that allows requesters (e.g., servers) to obtain local training models from workers (e.g., clients). Since workers are typically unwilling to provide training services/models freely and voluntarily, many incentive mechanisms in FL are designed to incentivize participation by offering monetary rewards from requesters. However, existing studies neglect two crucial aspects of real-world FL scenarios. First, workers can possess inherent incompatibility characteristics (e.g., communication channels and data sources), which can lead to degradation of FL efficiency (e.g., low communication efficiency and poor model generalization). Second, the requesters are budgeted, which limits the amount of workers they can hire for their tasks. In this paper, we investigate the scenario in FL where multiple budgeted requesters seek training services from incompatible workers with private training costs. We consider two settings: the cooperative budget setting where requesters cooperate to pool their budgets to improve their overall utility and the non-cooperative budget setting where each requester optimizes their utility within their own budgets. To address efficiency degradation caused by worker incompatibility, we develop novel compatibility-aware incentive mechanisms, CARE-CO and CARE-NO, for both settings to elicit true private costs and determine workers to hire for requesters and their rewards while satisfying requester budget constraints. Our mechanisms guarantee individual rationality, truthfulness, budget feasibility, and approximation performance. We conduct extensive experiments using real-world datasets to show that the proposed mechanisms significantly outperform existing baselines.

The Stackelberg security game is played between a defender and an attacker, where the defender needs to allocate a limited amount of resources to multiple targets in order to minimize the loss due to adversarial attacks by the attacker. While allowing targets to have different values, classic settings often assume uniform requirements for defending the targets. This enables existing results that study mixed strategies (randomized allocation algorithms) to adopt a compact representation of the mixed strategies. In this work, we initiate the study of mixed strategies for security games in which the targets can have different defending requirements. In contrast to the case of uniform defending requirements, for which an optimal mixed strategy can be computed efficiently, we show that computing the optimal mixed strategy is NP-hard for the general defending requirements setting. However, we show strong upper and lower bounds for the optimal mixed strategy defending result. Additionally, we extend our analysis to study uniform attack settings on these security games. We propose an efficient close-to-optimal Patching algorithm that computes mixed strategies using only a few pure strategies. Furthermore, we study the setting when the game is played on a network and resource sharing is enabled between neighboring targets. We show the effectiveness of our algorithm in various large real-world datasets, addressing both uniform and general defending requirements.

During loading and unloading steps, energy is consumed when cranes lift containers, while energy is often wasted when cranes drop containers. By optimizing the scheduling of cranes, it is possible to reduce energy consumption, thereby lowering operational costs and environmental impacts. In this paper, we introduce a single-crane scheduling problem with energy savings, focusing on reusing the energy from containers that have already been lifted and reducing the total energy consumption of the entire scheduling plan. We establish a basic model considering a one-dimensional storage area and provide a systematic complexity analysis of the problem. First, we investigate the connection between our problem and the semi-Eulerization problem and propose an additive approximation algorithm. Then, we present a polynomial-time Dynamic Programming (DP) algorithm for the case of bounded energy buffer and processing lengths. Next, adopting a Hamiltonian perspective, we address the general case with arbitrary energy buffer and processing lengths. We propose an exact DP algorithm and show that the variation of the problem is polynomially solvable when it can be transformed into a path cover problem on acyclic interval digraphs. We introduce a paradigm that integrates both the Eulerian and Hamiltonian perspectives, providing a robust framework for addressing the problem.