arXiv subjects

Xiaowei Wu

Publications and source records attributed to Xiaowei Wu.

At least 19 recordsLinked to original sources

arXiv2026

Best-of-Many-Worlds MMS Allocation for Chores with Sublinear Disposals

We study randomized allocations (lotteries) of indivisible chores under additive costs and introduce the notion of MMS1, which requires each agent's bundle to satisfy the maximin share (MMS) bound after the removal of at most one chore. Our main result establishes that every instance admits an ex-ante proportional lottery in whose support every allocation is MMS1 and all but $o(n)$ agents satisfy MMS. Consequently, every realized allocation can be made MMS by disposing of at most $o(n)$ chores. The proposed framework further achieves ex-ante proportionality alongside ex-post $4/3$-MMS, $o(n)$-AMMS, or $1$-out-of-$d$ MMS for $d=(1-o(1))n$. These guarantees substantially improve upon state-of-the-art bounds for MMS allocation for chores with disposal or subsidy, best-of-both-worlds fairness, approximate AMMS, and ordinal MMS approximations.

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arXiv2026

MMS Allocation for Chores with Item Disposals

Web platforms organize collective work, including content review and community maintenance, that imposes heterogeneous effort costs on participants. Fairly distributing these burdens while leaving as few tasks unassigned as possible is a natural objective for the design of such platforms. We study this through the maximin share (MMS) allocation problem with chore disposals under nonnegative additive costs. Our goal is to minimize the number of unassigned chores while guaranteeing every agent her MMS benchmark from the original instance. We prove that, for every instance with $n \ge 4$ agents, at most $n-3$ chore disposals suffice. We improve the bound of $2m/11+n$ disposals established by Barman et al. (2025), where $m$ is the number of chores, and eliminate the dependence on $m$. For four agents, we obtain a tight bound: one disposal always suffices, whereas known instances admit no complete MMS allocation (Ezra and Garbuz, 2026). We also prove the same result for goods: $n-3$ duplications suffice to ensure MMS.

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arXiv2026

Mean-only Prophet Inequalities

We study mean-based algorithms for single-choice prophet inequalities: the algorithm knows the number of variables and the mean of their maximum, but not their distributions. For arbitrary independent variables in a fixed order, we can already achieve the optimal $1/2$ competitive ratio using only this mean. For i.i.d. variables and prophet secretary, however, we previously knew only a $1-1/e$ guarantee, which is far away from the ratios with full distribution information. We improve the guarantees in both settings using a simple and natural algorithm: we fix a continuous decreasing threshold function that depends only on the mean and accept the first variable exceeding its threshold. For i.i.d. variables, we prove a $0.7419$ competitive ratio. For the prophet secretary, we prove a $0.6902$ competitive ratio.

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arXiv2026

Four-Level Quantized Soft Information Aided Hard-Decision Decoder for Product-like Codes

We propose a novel low-complexity soft-aided hard-decision decoding scheme for product-like codes, termed iterative bounded-distance decoding (iBDD) with graded scaled reliability and bit-flipping (GSRF). This scheme operates on four-level quantized soft information. It incorporates a graded scaled reliability rule to assign decoding confidence to the bounded-distance decoding result, and employs a bit-flipping rule based on bit-level and component-code-level reliability. A selective re-decoding rule is designed to further facilitate the error performance while keeping the number of BDD attempts in reasonably low levels. The decoding parameter design of iBDD-GSRF is investigated for product codes and staircase codes, respectively. Simulation results on both codes verify that iBDD-GSRF achieves a gain of more than 0.4 dB over the conventional iBDD, comparable to several existing unquantized soft-aided decoders.

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arXiv2026

Iterative Bounded Distance Decoding With 2-Bit Reliability Marker For Product-Like Codes

We propose a novel soft-aided hard-decision decoding scheme for product codes based on two-bit quantized reliability markers. In particular, one bit is used for a two-level tolerance miscorrection check to validate the bounded distance decoding (BDD) result, while the other identifies bits to be randomly flipped upon BDD failure and miscorrection. List decoding is incorporated to further facilitate the error performance. Density evolution is performed for the design of the quantization thresholds. Compared to iterative BDD, the proposed scheme requires only moderate increases in memory and computational overhead. Simulation results verify that our scheme outperforms several unquantized soft-aided decoders, while maintaining small memory costs and low BDD attempts.

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arXiv2026

Randomized Algorithm for MMS Allocation of Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores among $n$ agents in the agent-arrival model against an oblivious adversary. The chore set and the number of agents are known in advance. When agent $i$ arrives, her nonnegative additive cost function $c_i$ is revealed, and the algorithm must immediately and irrevocably assign her a subset of the unallocated chores. We focus on the notion of maximin share (MMS) and measure the fairness of the realized allocation $X$ by the ex-post MMS approximation ratio $ρ(X)$. We measure an algorithm's performance by its expected ratio, and also the guarantees that hold with high probability. For binary additive costs, we achieve an expected ex-post MMS ratio of $3/2+o(1)$, and show that every randomized online algorithm has an expected ratio of at least $3/2-o(1)$. For every $n$, the expected ratio is at most $1.755$. A variant of our algorithm guarantees an approximation ratio of $2$ with high probability, which is optimal. % For general additive costs, we present a weighted-rounding algorithm that achieves an expected ratio of $2+o(1)$, which also holds with high probability. The expected ratio is at most $2.594$ for every $n$. We also show that similar algorithms extend to additive goods, achieving a constant expected ex-post MMS ratio and guaranteeing every agent an $x$-fraction of her MMS with probability at least $1-85x^2$ for every $x\le1/15$.

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arXiv2026

Truthful-in-Expectation MMS Allocations for Chores

We study truthful-in-expectation (TIE) mechanisms for allocating indivisible chores alongside ex-post maximin share (MMS) guarantees. For goods, Bu and Tao (FOCS 2025) established a (1/n)-approximation for TIE mechanisms, and this was substantially improved by Babaioff, Feige, and Manaker Morag (FOCS 2026), who established an Ω(1/\log n) approximation, where n is the number of agents. The corresponding problem for chores has received less attention. The best-known result is due to Aziz, Li, and Wu (MAPR 2024), who gave a TIE mechanism with an O(\sqrt{\log n}) MMS approximation guarantee that holds only in expectation. They also established a 6/5 lower bound for TIE mechanisms for two agents. In this paper, we present the first TIE mechanism for chores that achieves a constant ex-post MMS approximation guarantee. Specifically, our mechanism guarantees an ex-post ratio of 1.97 for any number of agents n, which improves to 4/3 for n=2 and 3/2 for n=3. On the hardness side, we tighten the two-agent lower bound to 4/3, showing that our mechanism is optimal for n=2. More generally, we establish a lower bound of 13/12 on the ex-post MMS approximation ratio achievable by TIE mechanisms for every n\ge 3.

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arXiv2026

Tight Subsidy Bounds for Weighted Proportional Allocation of Mixed Manna

We study the problem of fairly allocating m indivisible items among n agents with possibly unequal entitlements in the mixed manna setting, where each item may be perceived as a good or a chore by different agents. We focus on the fundamental fairness notion of proportionality. Since proportional allocations need not exist in this setting, we allow monetary subsidies to restore proportionality while minimizing the total subsidy. When each item's (dis)utility is bounded by 1, a total subsidy of at least τ(n) \approx n/4 may be necessary. For goods-only or chores-only instances, the best previously known upper bound was n/3-1/6 due to Wu and Zhou~(2024). We close this gap by proving that a total subsidy of at most τ(n) always suffices, thereby establishing the tight subsidy bound. Our results hold even in the more general setting of weighted mixed manna, resolving an open question posed by~Wu et al. (2023) and Garg et al. (2026). The allocation also satisfies weighted proportionality up to one item (WPROP1). Our proof develops a novel application of the Knaster-Kuratowski-Mazurkiewicz (KKM) fixed-point theorem, extending the KKM framework to share-based fairness notions. Finally, we design a polynomial-time algorithm to compute such allocations for any fixed number of agents.

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arXiv2026

Revisiting EFX and fPO Allocations for Binary Chores

We study fair and efficient allocations of indivisible chores under binary additive costs, with a focus on unequal entitlements and best-of-both-worlds guarantees. While binary valuations have been extensively studied for goods, their chore counterpart remains much less understood. A notable exception is due to Tao et al. (TCS 2025), who established that EFX and fPO are compatible for binary chores with equal entitlements. We revisit binary chores under unequal entitlements and establish the computation of allocations that satisfy WEFX and fPO. Our key technical contribution is a new lexicographic potential function tailored to chores: any allocation minimizing this potential ensures both WEFX and fPO. This potential further guides a polynomial-time local-search algorithm for computing allocations with such fairness and efficiency guarantees. For best-of-both-worlds guarantees, we show that unequal entitlements create a sharp obstruction: even with two agents and identical binary additive costs, no lottery can simultaneously satisfy ex-ante WEF and ex-post WEF1. In contrast, for equal entitlements, we construct in polynomial time a lottery that is ex-ante EF and fPO, while every realization is both EFX and fPO.

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arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $α$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+ε}k, \log m\})$ for any constant $ε> 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

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arXiv2026

When Maximum Nash Welfare Becomes Strongly Fair: Bi-valued Goods

For the fair allocation of indivisible goods, the milestone work of Caragiannis et al. (2019) revolutionized the understanding of Maximum Nash Welfare (MNW) allocations by revealing their "unreasonable" ability to balance fairness (EF1) and efficiency (PO) for general additive functions. Subsequent work established that MNW allocations simultaneously satisfy EFX and GMMS (and consequently MMS and PMMS) for binary instances (Amanatidis et al. 2021 and Barman et al. 2018), and satisfy EFX for bi-valued instances (Amanatidis et al. 2021). In this paper, we revisit the (personalized) bi-valued instances and provide a tight characterization of the approximation guarantees of MNW allocations with respect to EFX, PMMS, and GMMS, showing that these guarantees are significantly stronger than what is known for general valuations. Furthermore, we demonstrate that even for the slightly more general setting of tri-valued instances, the fairness guarantees of MNW deteriorate significantly, which establishes a sharp boundary on the instances for which MNW allocations are strongly fair.

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arXiv2026

Minimization Prophet Inequality with Bounded Costs

We study the cost-minimization prophet inequality problem, in which a decision-maker sequentially observes $n$ independent and identically distributed (IID) random variables. After each observation, the decision-maker must either accept the current realization and stop, or reject it and continue with the next variable. The goal is to minimize the selected value. Unlike the classical maximization setting, if none of the first $n-1$ values is accepted, the final realization must be selected. Esfandiari et al. (SIDMA 2017) showed that this problem does not admit constant-competitive online algorithms in general, which motivates subsequent work on restricted distribution classes, such as entire distributions (Livanos and Mehta, SODA 2024) and distributions with bounded extreme values (Livanos and Mehta, EC 2025). In this work, we focus on distributions with bounded support. For distributions supported on $[1,b]$, we characterize the competitive ratio of online algorithms as a function of both $b$ and $n$. We consider both distribution-aware and distribution-oblivious settings. In the distribution-aware case, we provide a nearly tight characterization of the optimal online algorithm, showing that its competitive ratio is at most $b^{(1-1/n)^n}$ for all $n\geq 2$. More significantly, we design a distribution-oblivious algorithm that achieves the same guarantee, with a sequence of predetermined thresholds that depend only on $b$ and $n$. Furthermore, we extend our analysis to the non-IID setting, where we show that a simple single-threshold algorithm attains an asymptotically optimal competitive ratio of $Θ(\sqrt{b})$.

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arXiv2026

Online Matching in Convex Bipartite Graphs

Online resource-allocation systems, like outpatient scheduling and spectrum allocation, often assign sequentially arriving requests to an ordered pool of scarce resources, where each request accepts a contiguous interval of feasible options. We study the resulting online matching problem on convex bipartite graphs under irrevocable decisions and adversarial arrivals. We first show that convexity alone does not improve the classic worst-case guarantee of 1-1/e, achieved by Ranking. We then consider the uniform-length model, in which every online request has exactly d consecutive offline neighbors. We propose Flip, which uses one random bit to commit ex-ante to either earliest-feasible assignment or latest-feasible assignment. Although either natural deterministic policy can waste capacity and be asymptotically only 1/2-competitive, we show that their randomized mixture is 2/3-competitive. This guarantee is tight for Flip and remains valid against a semi-adaptive adversary that observes the selected policy before choosing the arrival order. We also prove that no randomized online algorithm can achieve a competitive ratio strictly larger than 3/4 in the uniform-length model.

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arXiv2026

The Complexity of Minimizing Subsidies in Envy-Free House Allocation

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.

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arXiv2026

Fractional Fully Online Matching

This paper studies fractional matching on general graphs in the fully online model of Huang et al. (JACM 2020), in which all vertices arrive online and remain available for only a limited time. The algorithm must make irrevocable fractional matching decisions while the relevant vertices are simultaneously available. We extend the classic Water-Filling algorithm, also known as Balance and originally introduced by Kalyanasundaram and Pruhs (TCS 2000), to the fully online setting. Using an online primal-dual framework, we prove that the generalized Water-Filling algorithm achieves a competitive ratio of $2-\sqrt{2}\approx 0.586$ in the fully online model, and that this analysis is tight. To surpass the $2-\sqrt{2}$ barrier, we incorporate the ideas of eager matching and history-based pricing into Water-Filling. We show that the resulting algorithm achieves an improved competitive ratio of $0.599$, thereby establishing that Water-Filling is not optimal in the fully online setting. On the hardness side, we further improve the known upper bound for fractional fully online matching, reducing the previous best bound of $0.6297$ due to Eckl et al. (ORL 2021) to $0.6132$.

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arXiv2026

Online Matching with KIID Edge Arrivals

In the classic online stochastic matching proposed by Feldman et al. (FOCS 2009), there is a known bipartite type-graph, where one side of the graph is given offline. Upon the arrival of each online vertex, its type is sampled independently and identically from the other side of the type-graph. This model has been extensively studied over the past decade, yielding a rich body of theoretical results. In this paper, we initiate the study of an edge arrival model for online stochastic matching. In our model, the online edges are sampled independently and identically (KIID) from a known type-graph, which need not be bipartite. We first show that the Greedy algorithm cannot achieve a competitive ratio strictly better than $0.5$ while the Suggested Matching algorithm has a competitive ratio of $1-1/e$ under the assumption of integral arrival rates, matching its performance in the one-sided vertex arrival model. We then propose a two-stage algorithm that combines Greedy and Suggested Matching, and show that its competitive ratio is strictly higher than $1-1/e$ for integral arrival rates. While our algorithm is simple, its analysis is intricate and builds upon the Natural LP, which has been proven very powerful in vertex arrival models. Our result reveals that even in the more challenging edge arrival setting for general graphs, competitive ratios better than $1-1/e$ are still possible, given the known distributions.

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arXiv2026

Fair Division by Contribution: A Shapley Value Perspective

In many resource allocation problems, agents' valuations are best interpreted not as subjective preferences, but as the value they generate from receiving resources. Such valuations capture productivity, effectiveness, or technology, and may differ significantly across agents. In these settings, classical fairness notions such as proportionality or envy-freeness fail to reflect agents' heterogeneous contributions to the collective outcome. Motivated by this perspective, we introduce \emph{Shapley Value Fairness (SVF)} for the allocation of divisible goods without monetary transfers. SVF interprets an agent's entitlement as her expected marginal contribution to optimal social welfare, and uses the Shapley value of the associated welfare maximization game as a normative fairness benchmark. We position SVF relative to existing fairness notions and show that it provides a natural bridge between fairness and efficiency in contribution-based environments. Since exact implementation of the Shapley value is generally infeasible without transfers, SVF naturally leads to the problem of finding allocations that approximate this benchmark as well as possible. We provide a systematic worst-case analysis of the achievable Shapley approximation ratio. For general concave valuations, we establish a tight $Θ(\ln n)$ bound. For capped concave valuations with bounded demands, this bound improves to $Θ(\ln D)$, where $D$ is the maximum aggregate demand for any item. For linear valuations, we further refine the bound to $Θ(\min\{k, \ln γ, \ln n\})$ in terms of the number of agent types $k$ and the value fluctuation ratio $γ$, and show that all bounds are asymptotically tight. Regarding per-instance guarantees, we show that a near-optimal approximation allocation can be computed efficiently (with high probability) via sampling for general concave valuations.

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arXiv2026

Recent Advances in Spatially Coupled Codes: Overview and Outlook

The concept of spatial coupling is among the most significant breakthroughs in coding theory over the past decade. The excellent waterfall and error floor performance of spatially coupled codes has positioned them as promising coding candidates for future communication and data storage systems. This article presents an overview of recent advances in spatially coupled codes. In particular, we first review several representative examples of recently proposed spatially coupled codes and highlight their unique features that make them appealing for different applications. Next, we discuss the useful properties of spatially coupled codes and how to design good spatially coupled codes. The article concludes with some future research directions and open problems.

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