arXiv subjects

Guido Schäfer

Publications and source records attributed to Guido Schäfer.

At least 19 recordsLinked to original sources

arXiv2026

Tight Liquid Welfare Guarantees for Auctions with Budgets via LP Duality

We study the efficiency of auctions with budget-constrained bidders and derive tight price of anarchy (PoA) bounds for coarse correlated equilibria (CCE). To this end, we develop a general framework that reduces proving PoA guarantees to finding feasible solutions to the dual of a linear program. The LP is formulated over a small number of per-bidder equilibrium statistics, incorporates constraints implied by the auction setting and equilibrium behavior, and captures a novel smoothness notion tailored to budget-constrained environments; we provide a reduction from classical smoothness to this new notion. Our approach enables simple and tight PoA analyses across a broad range of auction formats. Using our framework, we obtain tight liquid welfare guarantees for simultaneous first-price, second-price, and all-pay auctions, simultaneous auctions with restricted uniform bidding interfaces, discriminatory and uniform price multi-unit auctions, and generalized first-price position auctions. Beyond budget-constrained settings, we derive new lower bounds for the budget-free uniform price auction and generalized second-price auction; in particular, our lower bound for the uniform price auction matches the upper bound of $3.146$ by de Keijzer et al. (2013).

cs.GT↗

arXiv2026

Improved Lower Bounds and Output Augmentation for Facility Location Mechanisms

We study the strategic facility location problem under the egalitarian objective, where a mechanism uses the reported locations of a set of agents in Euclidean space to select a facility location that minimizes the maximum distance to any agent. We restrict our attention to strategyproof mechanisms, ensuring that no agent can benefit from misreporting their location. As our main results, we prove an asymptotic lower bound of $1 + \sqrt{d/(2(d+1))}$ on the approximation ratio of any mechanism that is strategyproof in expectation in $\mathbb{R}^d$. We show that this barrier is driven by large populations by providing a randomized $\sqrt{2}$-approximate mechanism for the two-agent case. We then consider an output-augmented framework, which allows the facility to be placed outside the agents' restricted domain. For the setting where agents are restricted to a line but the facility can be anywhere in the plane, we design a deterministic strategyproof $\sqrt{2}$-approximate mechanism with a matching lower bound, showing that output augmentation can replace the need for randomness. For the setting where the agents' reports lie on the unit circle but the facility can be placed anywhere in $\mathbb{R}^2$ we introduce a randomized $3/2$-approximate mechanism that is group-strategyproof in expectation.

cs.GT↗

arXiv2026

Beyond Stability: Improved Efficiency Guarantees for $α$-Stable Matchings

Stable matching mechanisms are fundamental to market design but face an inherent tension between stability and social welfare optimality. We study a natural relaxation of stability, termed $α$-stability, which models agents as willing to deviate only when the potential improvement is sufficiently large. Under $α$-stability, no pair of agents can deviate and improve their valuations by more than a factor of $1/α$, with $α\in (0,1]$. We provide a complete characterization of the stability-efficiency tradeoff under asymmetric valuations. This tradeoff depends on the degree of asymmetry $μ\in (0,1]$, which bounds the ratio between agents' valuations for any pair. Our results show that relaxing stability can substantially improve achievable efficiency guarantees. We further present a polynomial-time algorithm that computes an $α$-stable matching attaining the best possible efficiency guarantee. For $α\le μ/(μ+1)$, our algorithm achieves 1-efficiency; for larger $α$, it computes an $α$-stable matching achieving at least $(1/α)\cdot μ/(μ+1)$ of the optimal social welfare. Remarkably, our algorithm inflates the values of an optimal matching and then applies the Gale-Shapley algorithm to the modified instance. Finally, we show that computing an optimal $α$-stable matching is NP-hard, even under slight relaxations of stability, i.e., for $α$ close to 1.

cs.GT↗

arXiv2026

Online Budget-Feasible Mechanism Design with Predictions

Augmenting the input of algorithms with predictions is an algorithm design paradigm that suggests leveraging a (possibly erroneous) prediction to improve worst-case performance guarantees when the prediction is perfect (consistency), while also providing a performance guarantee when the prediction fails (robustness). Recently, Xu and Lu [2022] and Agrawal et al. [2024] proposed to consider settings with strategic agents under this framework. In this paper, we initiate the study of budget-feasible mechanism design with predictions. These mechanisms model a procurement auction scenario in which an auctioneer (buyer) with a strict budget constraint seeks to purchase goods or services from a set of strategic agents, so as to maximize her own valuation function. We focus on the online version of the problem where the arrival order of agents is random. We design mechanisms that are truthful, budget-feasible, and achieve a significantly improved competitive ratio for both monotone and non-monotone submodular valuation functions compared to their state-of-the-art counterparts without predictions. Our results assume access to a prediction for the value of the optimal solution to the offline problem. We complement our positive results by showing that for the offline version of the problem, access to predictions is mostly ineffective in improving approximation guarantees.

cs.GT↗

arXiv2026

Online Flow Time Minimization with Gradually Revealed Jobs

We consider the problem of online preemptive scheduling on a single machine to minimize the total flow time. In clairvoyant scheduling, where job processing times are revealed upon arrival, the Shortest Remaining Processing Time (SRPT) algorithm is optimal. In practice, however, exact processing times are often unknown. At the opposite extreme, non-clairvoyant scheduling, in which processing times are revealed only upon completion, suffers from strong lower bounds on the competitive ratio. This motivates the study of intermediate information models. We introduce a new model in which processing times are revealed gradually during execution. Each job consists of a sequence of operations, and the processing time of an operation becomes known only after the preceding one completes. This models many scheduling scenarios that arise in computing systems. Our main result is a deterministic $O(m^2)$-competitive algorithm, where $m$ is the maximum number of operations per job. More specifically, we prove a refined competitive ratio in $O(m_1 \cdot m_2)$, where $m_1$ and $m_2$ are instance-dependent parameters describing the operation size structure. Our algorithm and analysis build on recent advancements in robust flow time minimization (SODA '26), where jobs arrive with estimated sizes. However, in our setting we have no bounded estimate on a job's processing time. Thus, we design a highly adaptive algorithm that gradually explores a job's operations while working on them, and groups them into virtual chunks whose size can be well-estimated. This is a crucial ingredient of our result and requires a much more careful analysis compared to the robust setting. We also provide lower bounds showing that our bounds are essentially best possible. For the special case of scheduling with uniform obligatory tests, we show that SRPT at the operation level is $2$-competitive, which is best possible.

cs.DS↗

arXiv2025

Optimal Type-Dependent Liquid Welfare Guarantees for Autobidding Agents with Budgets

Online advertising systems have recently transitioned to autobidding, allowing advertisers to delegate bidding decisions to automated agents. Each advertiser directs their agent to optimize an objective function subject to return-on-investment (ROI) and budget constraints. Given their practical relevance, this shift has spurred a surge of research on the liquid welfare price of anarchy (POA) of fundamental auction formats under autobidding, most notably simultaneous first-price auctions (FPA). One of the main challenges is to understand the efficiency of FPA in the presence of heterogeneous agent types. We introduce {type-dependent smoothness framework that enables a unified analysis of the POA in such complex autobidding environments. In our approach, we derive type-dependent smoothness parameters which we carefully balance to obtain POA bounds. This balancing gives rise to a POA-revealing mathematical program, which we use to determine tight bounds on the POA of coarse correlated equilibria (CCE). Our framework is versatile enough to handle heterogeneous agent types and extends to the general class of fractionally subadditive valuations. Additionally, we develop a novel reduction technique that transforms budget-constrained agents into budget-unconstrained ones. Combining this reduction technique with our smoothness framework enables us to derive tight bounds on the POA of CCE in the general hybrid agent model with both ROI and budget constraints. Among other results, our bounds uncover an intriguing threshold phenomenon showing that the POA depends intricately on the smallest and largest agent types. We also extend our study to FPAs with reserve prices, which can be interpreted as predictions of agents' values, to further improve efficiency guarantees.

cs.GT↗

arXiv2025

Mechanism Design with Outliers and Predictions

We initiate the study of mechanism design with outliers, where the designer can discard $z$ agents from the social cost objective. This setting is particularly relevant when some agents exhibit extreme or atypical preferences. As a natural case study, we consider facility location on the line: $n$ strategic agents report their preferred locations, and a mechanism places a facility to minimize a social cost function. In our setting, the $z$ agents farthest from the chosen facility are excluded from the social cost. While it may seem intuitive that discarding outliers improves efficiency, our results reveal that the opposite can hold. We derive tight bounds for deterministic strategyproof mechanisms under the two most-studied objectives: utilitarian and egalitarian social cost. Our results offer a comprehensive view of the impact of outliers. We first show that when $z \ge n/2$, no strategyproof mechanism can achieve a bounded approximation for either objective. For egalitarian cost, selecting the $(z + 1)$-th order statistic is strategyproof and 2-approximate. In fact, we show that this is best possible by providing a matching lower bound. Notably, this lower bound of 2 persists even when the mechanism has access to a prediction of the optimal location, in stark contrast to the setting without outliers. For utilitarian cost, we show that strategyproof mechanisms cannot effectively exploit outliers, leading to the counterintuitive outcome that approximation guarantees worsen as the number of outliers increases. However, in this case, access to a prediction allows us to design a strategyproof mechanism achieving the best possible trade-off between consistency and robustness. Finally, we also establish lower bounds for randomized mechanisms that are truthful in expectation.

cs.GT↗

arXiv2025

Partial Allocations in Budget-Feasible Mechanism Design: Bridging Multiple Levels of Service and Divisible Agents

Budget-feasible procurement has been a major paradigm in mechanism design since its introduction by Singer (2010). An auctioneer (buyer) with a strict budget constraint is interested in buying goods or services from a group of strategic agents (sellers). In many scenarios it makes sense to allow the auctioneer to only partially buy what an agent offers, e.g., an agent might have multiple copies of an item to sell, they might offer multiple levels of a service, or they may be available to perform a task for any fraction of a specified time interval. Nevertheless, the focus of the related literature has been on settings where each agent's services are either fully acquired or not at all. The main reason for this, is that in settings with partial allocations like the ones mentioned, there are strong inapproximability results. Under the mild assumption of being able to afford each agent entirely, we are able to circumvent such results in this work. We design a polynomial-time, deterministic, truthful, budget-feasible $(2+\sqrt{3})$-approximation mechanism for the setting where each agent offers multiple levels of service and the auctioneer has a discrete separable concave valuation function. We then use this result to design a deterministic, truthful and budget-feasible $O(1)$-approximation mechanism for the setting where any fraction of a service can be acquired and the auctioneer's valuation function is separable concave (i.e., the sum of concave functions). For the special case of a linear valuation function, we improve the best known approximation ratio for the problem from $1+ϕ$ (by Klumper & Schäfer (2022)) to $2$. This establishes a separation between this setting and its indivisible counterpart.

cs.GT↗

arXiv2025

The Effectiveness of Golden Tickets and Wooden Spoons for Budget-Feasible Mechanisms

One of the main challenges in mechanism design is to carefully engineer incentives ensuring truthfulness while maintaining strong social welfare approximation guarantees. But these objectives are often in conflict, making it impossible to design effective mechanisms. An important class of mechanism design problems that belong to this category are budget-feasible mechanisms. Here, the designer needs to procure services of maximum value from a set of agents while being on a budget, i.e., having a limited budget to enforce truthfulness. However, as empirical studies suggest, factors like limited information and bounded rationality question the idealized assumption that the agents behave perfectly rationally. Motivated by this, Troyan and Morill in 2022 introduced non-obvious manipulability (NOM) as a more lenient incentive compatibility notion. In this paper, we investigate whether resorting to NOM enables us to derive improved mechanisms in budget-feasible domains. We establish a tight bound of 2 on the approximation guarantee of budget-feasible mechanisms satisfying NOM for the general class of monotone subadditive valuation functions. Our result thus establishes a clear separation between the achievable guarantees for DSIC (perfectly rational agents) and NOM (imperfectly rational agents) as no truthful mechanism can achieve a guarantee better than 2.41. Along the way, we fully characterize BNOM and WNOM (which together form NOM) and derive matching upper and lower bounds, respectively. Conceptually, our characterization results suggest "Golden Tickets" and "Wooden Spoons" as natural means to realize BNOM and WNOM, respectively. Additionally, we show that randomized budget-feasible mechanisms satisfying BNOM can achieve an expected approximation ratio arbitrarily close to 1.

cs.GT↗

arXiv2024

Learning-Enhanced Neighborhood Selection for the Vehicle Routing Problem with Time Windows

Large Neighborhood Search (LNS) is a universal approach that is broadly applicable and has proven to be highly efficient in practice for solving optimization problems. We propose to integrate machine learning (ML) into LNS to assist in deciding which parts of the solution should be destroyed and repaired in each iteration of LNS. We refer to our new approach as Learning-Enhanced Neighborhood Selection (LENS for short). Our approach is universally applicable, i.e., it can be applied to any LNS algorithm to amplify the workings of the destroy algorithm. In this paper, we demonstrate the potential of LENS on the fundamental Vehicle Routing Problem with Time Windows (VRPTW). We implemented an LNS algorithm for VRPTW and collected data on generated novel training instances derived from well-known, extensively utilized benchmark datasets. We trained our LENS approach with this data and compared the experimental results of our approach with two benchmark algorithms: a random neighborhood selection method to show that LENS learns to make informed choices and an oracle neighborhood selection method to demonstrate the potential of our LENS approach. With LENS, we obtain results that significantly improve the quality of the solutions.

cs.LG↗

arXiv2024

To Trust or Not to Trust: Assignment Mechanisms with Predictions in the Private Graph Model

The realm of algorithms with predictions has led to the development of several new algorithms that leverage (potentially erroneous) predictions to enhance their performance guarantees. The challenge is to devise algorithms that achieve optimal approximation guarantees as the prediction quality varies from perfect (consistency) to imperfect (robustness). This framework is particularly appealing in mechanism design contexts, where predictions might convey private information about the agents. In this paper, we design strategyproof mechanisms that leverage predictions to achieve improved approximation guarantees for several variants of the Generalized Assignment Problem (GAP) in the private graph model. In this model, first introduced by Dughmi & Ghosh (2010), the set of resources that an agent is compatible with is private information. For the Bipartite Matching Problem (BMP), we give a deterministic group-strategyproof (GSP) mechanism that is $(1 +1/γ)$-consistent and $(1 + γ)$-robust, where $γ\ge 1$ is some confidence parameter. We also prove that this is best possible. Remarkably, our mechanism draws inspiration from the renowned Gale-Shapley algorithm, incorporating predictions as a crucial element. Additionally, we give a randomized mechanism that is universally GSP and improves on the guarantees in expectation. The other GAP variants that we consider all make use of a unified greedy mechanism that adds edges to the assignment according to a specific order. Our universally GSP mechanism randomizes over the greedy mechanism, our mechanism for BMP and the predicted assignment, leading to $(1+3/γ)$-consistency and $(3+γ)$-robustness in expectation. All our mechanisms also provide more fine-grained approximation guarantees that interpolate between the consistency and the robustness, depending on some natural error measure of the prediction.

cs.GT↗

arXiv2023

Round and Bipartize for Vertex Cover Approximation

The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a consequence, the natural rounding algorithm based on this relaxation computes an optimal solution for bipartite graphs and a $2$-approximation for general graphs. This raises the question of whether one can interpolate the rounding curve of the standard linear programming relaxation in a beyond the worst-case manner, depending on how close the graph is to being bipartite. In this paper, we consider a simple rounding algorithm that exploits the knowledge of an induced bipartite subgraph to attain improved approximation ratios. Equivalently, we suppose that we work with a pair $(G, S)$, consisting of a graph with an odd cycle transversal. If $S$ is a stable set, we prove a tight approximation ratio of $1 + 1/ρ$, where $2ρ-1$ denotes the odd girth (i.e., length of the shortest odd cycle) of the contracted graph $\tilde{G} := G /S$ and satisfies $ρ\in [2,\infty]$. If $S$ is an arbitrary set, we prove a tight approximation ratio of $\left(1+1/ρ\right) (1 - α) + 2 α$, where $α\in [0,1]$ is a natural parameter measuring the quality of the set $S$. The technique used to prove tight improved approximation ratios relies on a structural analysis of the contracted graph $\tilde{G}$. Tightness is shown by constructing classes of weight functions matching the obtained upper bounds. As a byproduct of the structural analysis, we obtain improved tight bounds on the integrality gap and the fractional chromatic number of 3-colorable graphs. We also discuss algorithmic applications in order to find good odd cycle transversals and show optimality of the analysis.

cs.DS↗

arXiv2023

Dijkstras algorithm with predictions to solve the single-source many-targets shortest-path problem

We study the use of machine learning techniques to solve a fundamental shortest path problem, known as the single-source many-targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to compute a shortest path from a given source node to any of several target nodes. Basically, our idea is to equip an adapted version of Dijkstras algorithm with machine learning predictions to solve this problem: Based on the trace of the algorithm, we design a neural network that predicts the shortest path distance after a few iterations. The prediction is then used to prune the search space explored by Dijkstras algorithm, which may significantly reduce the number of operations on the underlying priority queue. We note that our algorithm works independently of the specific method that is used to arrive at such predictions. Crucially, we require that our algorithm always computes an optimal solution (independently of the accuracy of the prediction) and provides a certificate of optimality. As we show, in the worst-case this might force our algorithm to use the same number of queue operations as Dijkstras algorithm, even if the prediction is correct. In general, however, our algorithm may save a significant fraction of the priority queue operations. We derive structural insights that allow us to lower bound these savings on partial random instances. In these instances, an adversary can fix the instance arbitrarily except for the weights of a subset of relevant edges, which are chosen randomly. Our bound shows that the number of relevant edges which are pruned increases as the prediction error decreases. We then use these insights to derive closed-form expressions of the expected number of saved queue operations on random instances.

cs.DS↗

arXiv2022

Budget Feasible Mechanisms for Procurement Auctions with Divisible Agents

We consider budget feasible mechanisms for procurement auctions with additive valuation functions. For the divisible case, where agents can be allocated fractionally, there exists an optimal mechanism with approximation guarantee $e/(e-1)$ under the small bidder assumption. We study the divisible case without the small bidder assumption, but assume that the true costs of the agents are bounded by the budget. This setting lends itself to modeling economic situations in which the goods represent time and the agents' true costs are not necessarily small compared to the budget. Non-trivially, we give a mechanism with an approximation guarantee of 2.62, improving the result of 3 for the indivisible case. Additionally, we give a lower bound on the approximation guarantee of 1.25. We then study the problem in more competitive markets and assume that the agents' value over cost efficiencies are bounded by some $θ\ge 1$. For $θ\le 2$, we give a mechanism with an approximation guarantee of 2 and a lower bound of 1.18. Both results can be extended to settings with different agent types with a linear capped valuation function for each type. Finally, if each agent type has a concave valuation, we give a mechanism for which the approximation guarantee grows linearly with the number of agent types.

cs.GT↗

arXiv2022

Corruption in Auctions: Social Welfare Loss in Hybrid Multi-Unit Auctions

We initiate the study of the social welfare loss caused by corrupt auctioneers, both in single-item and multi-unit auctions. In our model, the auctioneer may collude with the winning bidders by letting them lower their bids in exchange for a (possibly bidder-dependent) fraction $γ$ of the surplus. We consider different corruption schemes. In the most basic one, all winning bidders lower their bid to the highest losing bid. We show that this setting is equivalent to a $γ$-hybrid auction in which the payments are a convex combination of first-price and the second-price payments. More generally, we consider corruption schemes that can be related to $γ$-approximate first-price auctions ($γ$-FPA), where the payments recover at least a $γ$-fraction of the first-price payments. Our goal is to obtain a precise understanding of the robust price of anarchy (POA) of such auctions. If no restrictions are imposed on the bids, we prove a bound on the robust POA of $γ$-FPA which is tight (over the entire range of $γ$) for the single-item and the multi-unit auction setting. On the other hand, if the bids satisfy the no-overbidding assumption a more fine-grained landscape of the price of anarchy emerges, depending on the auction setting and the equilibrium notion. Albeit being more challenging, we derive (almost) tight bounds for both auction settings and several equilibrium notions, basically leaving open some (small) gaps for the coarse-correlated price of anarchy only.

cs.GT↗

arXiv2020

Maximum Coverage with Cluster Constraints: An LP-Based Approximation Technique

Packing problems constitute an important class of optimization problems, both because of their high practical relevance and theoretical appeal. However, despite the large number of variants that have been studied in the literature, most packing problems encompass a single tier of capacity restrictions only. For example, in the Multiple Knapsack Problem, we assign items to multiple knapsacks such that their capacities are not exceeded. But what if these knapsacks are partitioned into clusters, each imposing an additional capacity restriction on the knapsacks contained in that cluster? In this paper, we study the Maximum Coverage Problem with Cluster Constraints (MCPC), which generalizes the Maximum Coverage Problem with Knapsack Constraints (MCPK) by incorporating cluster constraints. Our main contribution is a general LP-based technique to derive approximation algorithms for cluster capacitated problems. Our technique allows us to reduce the cluster capacitated problem to the respective original packing problem. By using an LP-based approximation algorithm for the original problem, we can then obtain an effective rounding scheme for the problem, which only loses a small fraction in the approximation guarantee. We apply our technique to derive approximation algorithms for MCPC. To this aim, we develop an LP-based $\frac12(1-\frac1e)$-approximation algorithm for MCPK by adapting the pipage rounding technique. Combined with our reduction technique, we obtain a $\frac13(1-\frac1e)$-approximation algorithm for MCPC. We also derive improved results for a special case of MCPC, the Multiple Knapsack Problem with Cluster Constraints (MKPC). Based on a simple greedy algorithm, our approach yields a $\frac13$-approximation algorithm. By combining our technique with a more sophisticated iterative rounding approach, we obtain a $\frac12$-approximation algorithm for certain special cases of MKPC.

cs.DS↗

arXiv2020

Topological Price of Anarchy Bounds for Clustering Games on Networks

We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their strategy with their neighbors. The goal of a player is to choose a strategy that maximizes her utility given the strategies of her neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy: A large inefficiency between the total utility generated in centralized outcomes and equilibrium outcomes in which players selfishly try to maximize their utility. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erdős-Rényi random graphs (where every possible edge in the network is present with a fixed probability), which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds.

cs.GT↗

arXiv2019

Cost Sharing over Combinatorial Domains: Complement-Free Cost Functions and Beyond

We study mechanism design for combinatorial cost sharing. Imagine that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost sharing domains until recently \cite{DobzinskiO17}. The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations of cost functions which capture the behavior of their average cost-shares. Based on our trace-monotonicity property, we design a scheme of ascending cost sharing mechanisms which is applicable to the combinatorial cost sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, $O(1)$-budget-balanced and $O(H_n)$-approximate with respect to the social cost. Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general only guarantees a poor social cost approximation of $n$. We identify conditions under which the mechanism achieves improved social cost approximation guarantees.

cs.GT↗