We consider the problem of allocating a set of indivisible goods to a set of strategic agents with arbitrary weights. While truthful mechanism is hard to guarantee any non-trivial fairness, Amanatidis et al. (WINE 2021 and MOR 2024) studied the fairness guarantees of the equilibria of the Round-Robin mechanism. They show that when all agents have the same weight, every pure Nash equilibrium of Round-Robin leads to an envy-free up to one item (EF1) allocation, with respect to agents' true valuations. In this paper, we investigate the weighted setting where agents are asymmetric and study the weighted picking sequence protocol, which is a natural extension of Round-Robin in the weighted setting. More specifically, we show that the weighted picking sequence protocol always has pure Nash equilibria and all the corresponding allocations are weighted EF1 with respect to the true valuation functions for two agents.
We study the facility location problem in the context of individual fairness to propose the Individual Preference Facility Location (IPFL) problem. In the vanilla facility location problem, the goal is to select a subset of facilities to serve all clients while minimizing total opening and connection costs. IPFL aims to optimize the facility location objective while meeting individual preferences by requiring that each client is served by a facility within its fair radius. The fair radius is defined as the distance between a client and its τ -th nearest neighbor, where τ is a carefully designed parameter. IPFL balances facility load by opening more facilities in dense areas. However, a few clients may disproportionately affect the final costs or violate the individual preference constraints. To address this, we extend IPFL to its outlier variant, IPFLO, where up to m clients can remain unserved. As our contribution, we provide 2-approximation algorithms for both IPFL and IPFLO using a dual fitting technique.
This work focuses on the strategyproofness of voting systems in which voters select multiple options from a set of possibilities. These systems include those that are used for Participatory Budgeting, where elections are held to determine the allocation of a community budget (e.g., city or regional level) for funding various projects. We present a model for analyzing voting mechanisms and the Constrained Change Property (CCP), which serves as a criterion for designing strategyproof voting mechanisms. Additionally, we define a new concept of a social choice function and leverage it to develop a new class of utilitarian voting mechanisms, referred to as score voting. We prove that the mechanisms designed with core voting with a neutral score function are equivalent to knapsack voting on the same instance. Furthermore, we demonstrate that a score voting mechanism based on a total score function is strategyproof if and only if its score function satisfies CCP. Building on these findings, we propose an algorithm capable of identifying the closest total score function that ensures the strategyproofness of any given score voting mechanism.
We study the stable matching problem with partial information, where agents submit only partial approval preferences, and the goal is to find a matching that is as stable as possible in the worst-case scenario. Unlike previous studies that focus solely on the Stable Marriage setting and measure stability by the number of blocking pairs, we explore another well-explored stability measure: the number of blocking agents. Additionally, we extend our analysis to both the Stable Roommates and Hospital/Residents problems. Our findings offer a comprehensive view of the computational complexity across these problem variants, highlighting interesting contrasts between blocking agents and blocking pairs, as well as among the three stable matching settings.
This paper investigates waitlist mechanisms for public housing allocation, introducing the pay-per-offer mechanism as a novel alternative to the deferral-based approach. Through a Markov decision process, dynamically arriving items are allocated to waiting agents with heterogeneous values for different items and diverse outside options. Key contributions include analysis of optimal strategies for agents in these mechanisms, evaluation of how evaluation metrics vary based on the distribution of outside options and waitlist parameters. We provide valuable insights into the design and impact of various waitlist mechanisms.
We consider a scenario where a group of agents needs to elect a committee to lead them in accomplishing a project. They elect a committee to maximize social welfare, and the question is how to distribute the total value of the project to every agent. This scenario encodes a cooperative game setting where the reward of the chosen coalition must be distributed fairly. First, we establish the axiomatic foundation of solution concepts in this cooperative committee election game. We show that a natural extension of Shapley value to this game does not meet the classical axioms when the values of different coalitions are binary. We then propose a value distribution rule that satisfies all the desired properties. Furthermore, we prove that this rule is unique in meeting these properties and also satisfies an additional monotonicity property. When the values of the coalitions can take any general values, we decompose the game into a linear combination of simple games. This decomposition is unique, allowing us to extend our value distribution rule to solve this general class of games.
Data sharing is widely regarded as a critical approach to unlocking the value of data, encompassing data rights management, processing, and profit allocation. However, existing methods often suffer from fragmented designs, incompatible assumptions, and security challenges, perpetuating the issue of data silos. To address these limitations, we propose Transaction-Based Data Sharing (TBDS), a comprehensive and modular solution. TBDS adopts a formal-language-based data rights management module, maintaining compatibility across modules and enabling efficient permission verification and state updates. It leverages blockchain and Trusted Execution Environments (TEEs) to ensure secure operations while handling remote attestation internally, eliminating reliance on external parties. Furthermore, TBDS introduces a transaction-driven workflow, where smart contracts facilitate seamless interactions between modules. Finally, we design a chain-based profit allocation mechanism that balances incentives and privacy, ensuring fair and transparent distribution of rewards among participants. We also show that this mechanism improves participants' revenue. With these innovations, TBDS not only addresses the challenges of fragmented designs and security risks but also establishes a scalable and incentive-compatible framework, paving the way for more efficient and secure datasharing ecosystems.
The Maximum k-Balanced Weighted Biclique problem looks for a biclique in the given vertex-weighted bipartite graph such that the weight of the biclique is maximized, and the gap between the weights of the two independent vertex sets of the biclique is at most the given value k. Within the paper, we propose an exact algorithm for the problem with a new perspective: feedback vertex set. Specifically, our approach begins by conducting branch operations on the vertices with large degree and the ones in the feedback vertex set of the considered bipartite graph G, then calls a polynomial-time algorithm proposed for a related problem to each resulting graph that is acyclic. Our algorithm is shown to have time complexity O(min{1.325^n, 2^2δ (G)} n^4 W^4_max) , where n and W_max are the number and maximum weight of the vertices in G, respectively, and δ (G) is the minimum cardinality (i.e., number of vertices) of a feedback vertex set for G. Furthermore, our algorithm can be adapted to solve the Maximum Balanced Biclique problem (i.e., k=0 and G is unweighted) with time complexity O(min{1.325^n, 2^2δ (G)} n^2log ^6 n) , which is better than the best-known time complexity O(1.3803^n n^2) , especially if G satisfies δ (G) ≤ n/5 .
In this paper, we propose two string problems, and study algorithms and complexity of various versions for those problems. Let S={s_1, s_2, … , s_m} be a set of m strings. A common substring of S is a substring appearing in every string in S. Given a set of m strings S={s_1, s_2, … , s_m} and a positive integer k, we want to find a set C of k common substrings of S such that the k common substrings in C appear in the same order and have no overlap among the m input strings in S, and the total length of the k common substring in C is maximized. This problem is referred to as the longest total length of k common substrings from m input strings (LCSS(k, m) for short). The other problem we study here is called the longest total length of a set of common substrings with length more than l from m input string (LSCSS(l, m) for short). Given a set of m strings S={s_1, s_2, … , s_m} and a positive integer l, for LSCSS(l, m), we want to find a set of common substrings of S, each is of length more than l, such that the total length of all the common substrings is maximized. We show that both problems are NP-hard when k and m are variables. We propose dynamic programming algorithms with time complexity O(k n_1n_2) and O(n_1n_2) to solve LCSS(k, 2) and LSCSS(l, 2), respectively, where n_1 and n_2 are the lengths of the two input strings. We then design an algorithm for LSCSS(l, m) when every length >l common substring appears once in each of the m-1 input strings. The running time is O(n^2_1m) , where n_1 is the length of the input string with no restriction on length >l common substrings. Finally, we propose a fixed parameter algorithm for LSCSS(l, m), where each length > l common substring appears m -1 + c times among the m- 1 input strings (other than s_1 ). In other words, each length > l common substring may repeatedly appear at most c times among the m-1 input strings {s_2, s_3, … , s_m} . The running time of the proposed algorithm is O((n_12^c)^2m) , where n_1 is the input string with no restriction on repeats. The LSCSS(l, m) is proposed to handle whole chromosome sequence alignment for different strains of the same species, where more than 98% of letters in core regions are identical.
We establish the first theoretical results for scheduling with testing on a single machine and on identical parallel machines to minimize the total weighted completion time in the adversarial model. We present a deterministic algorithm with a competitive ratio of 2.3166 for single-machine scheduling and show that a randomized variant has a competitive ratio of 2.1523. These algorithms, combined with list scheduling, yield competitive ratios of 2.7763 and 2.5110 for identical parallel machine scheduling.
Generalized assignment is one of the constraints that has been widely studied in fair allocation problems. Existing research has mostly focused on (approximate) envy-freeness. In this work, we consider the maximin share (MMS) fairness. It has been observed that under generalized assignment constraints, the agents’ valuations are fractionally subadditive and thus a 3/13(≈ 0.230) -approximate MMS fair allocation exists, as shown by Akrami et al. [NeurIPS 2023]. In this paper, we improve the approximation ratio to 4/15≈ 0.266 . For the case of two agents, we improve the approximation to 2/3 , and prove that this bound is tight.
We study a variation of the facility location problem that involves finding ideal locations for capacitated facilities and assigning agents to these facilities. Additionally, each agent has an ordinal ranking over the facilities and incurs a cost related to both the ranking and the distance from their assigned facility. Our work focuses on minimizing the maximum cost and total cost. For these objectives, we show that computing an optimal solution is intractable in general, but we provide exact algorithms that run in polynomial time when the number of facilities is constant. We then move to the mechanism design setting, where the agents' preferences are private information, and design strategy-proof mechanisms which have a bounded approximation for our objectives.
In this paper, we investigate randomly terminating two-player zero-sum Markov games. This game model differs from infinite-horizon discounted zero-sum Markov games and can be used to model many practical scenarios; however, related work on such games is still insufficient. We propose the regularized minimax-V learning algorithm and prove that the value sequence generated by this algorithm converges to the minimax value function with an appropriate choice of regularization parameter sequence. This algorithm applies the Euclidean regularization technique to accelerate the convergence in a different way compared with previous literature. Through simulation experiments, we demonstrate the convergence of regularized minimax-V learning algorithm in the ratio game and a randomly generated Markov game. To the best of our knowledge, for randomly terminating two-player zero-sum Markov games, this paper presents the first accelerated NE-solving algorithm.
In this paper, we investigate the approximation and parameterized complexities of MAXNAESAT variants. We begin by presenting a simple yet rigorous proof establishing the APX-completeness of the MAXNAE2SAT problem. Notably, APX-completeness holds even when the repetition factor of each variable is bounded by 3, i.e., each variable appears in at most three clauses in the MAXNAE2SAT instance. Our APX-completeness proof is a strict reduction that directly establishes a new inapproximability bound for the MAXNAE2SAT problem. The decision version of MAXNAE2SAT remains NP-complete when the repetition factor of each variable is bounded by 3, mirroring the NP-completeness of MAXCUT in cubic graphs. We further establish a tight computational dichotomy by proving that the MAXNAE2SAT problem is solvable in linear time when the repetition factor of each variable is bounded by 2. Finally, we present a fixed-parameter tractable algorithm for MAXNAE2SAT instances where the repetition factor of each variable is bounded by 3.
The target-constrained mixed graph covering (TMGC) problem considers a graph where edges and vertices are each assigned a cost and a weight. The goal is to select a minimum-cost subset of vertices and edges subject to the covering-target constraint that its covered weight (i.e., the total weight of the selected vertices, selected edges, and edges incident to the selected vertices) meets or exceeds a given threshold. This problem models real-world scenarios, like optimizing the removal of facilities (vertices) and roads (edges) in a network while ensuring the value of the remaining network (including the value of remaining facilities and their connecting roads) remains below a specified limit. From a theoretical perspective, this TMGC model extends the weighted partial vertex cover problem in two significant ways: it incorporates covering weights for both edges and vertices, and it allows a direct selection of edges alongside vertices to satisfy the covering target. Despite this increased complexity and generality compared to (the partial version of) the classic vertex cover problem, we develop a 2-approximation primal-dual algorithm for TMGC, whose ratio 2 matches the known lower bound for the simpler vertex cover problem.
We consider an auction-based crowdsourcing system. A requester is faced with a binary choice question and decides to hire workers to answer the question. The workers can ask prices for answering the question and the requester can choose to hire which workers based on their skills and ask prices. We model the problem as a mechanism design problem and characterize the optimal hiring policy. We show that the problem of computing the accuracy of a given set of workers is #P-hard. However, we prove that choosing at most k workers into committee can achieve at least 1/⌈ n/k ⌉ of the optimal utility. Finally, we also provide a polynomial algorithm for computing the optimal hiring strategy when the number of workers’ skill levels is constant.
In this paper, we introduce the subinterval cover problem. Given a set of interval candidates, each associated with a specific cost factor, we need to select a subinterval from each candidate to cover the entire range. The cost of selecting a subinterval in a candidate interval is determined by multiplying the selected length by the cost factor (the weight). Our goal is to minimize the total cost. This problem has broad applications, such as drone delivery and robot motion planning. Our first finding is that a natural LP formulation of the problem has an unbounded integrality gap, which highlights the challenge of studying this problem. Second, we develop polynomial-time dynamic programming algorithms for two special cases: 1) two distinct cost factors; 2) a constant number of distinct cost factors, and the interval candidates form a laminar set family: each pair of intervals is either disjoint, or one interval contains the other. As a corollary of our dynamic programming algorithm, we design a polynomial-time √(w_max/w_min) -approximation algorithm for the general cases, where w_max and w_min are the maximum and minimum weights of the intervals, respectively.
In this paper, we study the online power cover problem on a line. Suppose L is a line on the plane, and S is a set of sensors on the line L, and each sensor can deploy a power and generate a covered area that can cover users. This problem is to find a minimum power assignment to cover a sequence of users on the line L arriving one by one. In this paper, we first prove that the lower bound is 2 for this problem even when |S|=2 . Then, we present an online algorithm with a competitive ratio that is no more than |S| based on the greedy technique. Note that, this algorithm is the best possible online algorithm for this problem with |S|=2 . Finally, we consider a special case of this problem, in which S={s_0,s_1,s_2} and d(s_0,s_1)=d(s_1,s_2) , and present an online algorithm with a competitive ratio that is no more than √(2)+1 .
The rapid advancement of AI and other emerging technologies has triggered exponential growth in computing resources demand. Faced with prohibitive infrastructure costs for large-scale computing clusters, users are increasingly resorting to leased computing resources from third-party providers. However, prevalent overestimation of operational requirements frequently leads to substantial underutilization of the computing resources. To mitigate such inefficiency, we propose a contract-based incentive framework for computing resources repurchasing. Comparing to auction mechanisms, our design enables providers to reclaim and reallocate surplus computing resources through market-driven incentives. Our framework operates in a multi-parameter environment where both clients' idle resource capacities and their unit valuations of retained resources are private information, posing a significant challenge to contract design. Two scenarios are considered based on whether all clients possess the same amount of idle resource capacity. By transforming the contract design problem into solving a mathematical program, we obtain the optimal contracts for each scenario, which can maximize the utility of computing resources providers while ensuring the requirements of incentive compatibility (IC) and individual rationality (IR). This innovative design not only provides an effective approach to reduce the inefficient utilization of computing resources, but also establishes a market-oriented paradigm for sustainable computing ecosystems.
This paper studies mechanism design for auctions with externalities on budgets, a novel setting where the budgets that bidders commit are adjusted due to the externality of the competitors' allocation outcomes-a departure from traditional auctions with fixed budgets. This setting is motivated by real-world scenarios, for example, participants may increase their budgets in response to competitors' obtained items. We initially propose a general framework with homogeneous externalities to capture the interdependence between budget updates and allocation, formalized through a budget response function that links each bidder's effective budget to the amount of items won by others. The main contribution of this paper is to propose a truthful and individual rational auction mechanism for this novel auction setting, which achieves an approximation ratio of 1/3 with respect to the liquid welfare. This mechanism is inspired by the uniform-price auction, in which an appropriate uniform price is selected to allocate items, ensuring the monotonicity of the allocation rule while accounting for budget adjustments. Additionally, this mechanism guarantees a constant approximation ratio by setting a purchase limit. Complementing this result, we establish an upper bound: no truthful mechanism can achieve an approximation ratio better than 1/2. This work offers a new perspective to study the impact of externalities on auctions, providing an approach to handle budget externalities in multi-agent systems.
