Stefano Leonardi

TCS Journal 2026 Journal Article

Fair division with interdependent values

• Georgios Birmpas
• Tomer Ezra
• Stefano Leonardi
• Matteo Russo

We introduce the study of designing allocation mechanisms for fairly allocating indivisible goods in settings with interdependent valuation functions. In our setting, there is a set of goods that needs to be allocated to a set of agents (without disposal). Each agent is given a private signal, and his valuation function depends on the signals of all agents. Without the use of payments, there are strong impossibility results for designing strategyproof allocation mechanisms even in settings without interdependent values. Therefore, we turn to design mechanisms that always admit equilibria that are fair with respect to their true signals, despite their potentially distorted perception. To do so, we first extend the definitions of pure Nash equilibrium and well-studied fairness notions in literature to the interdependent setting. We devise simple allocation mechanisms that always admit a fair equilibrium with respect to the true signals. We complement this result by showing that, even for very simple cases with binary additive interdependent valuation functions, no allocation mechanism that always admits an equilibrium, can guarantee that all equilibria are fair with respect to the true signals.

TCS Journal 2026 Journal Article

Submodular maximization subject to a knapsack constraint: Combinatorial algorithms with near-optimal adaptive complexity

• Georgios Amanatidis
• Federico Fusco
• Philip Lazos
• Stefano Leonardi
• Alberto Marchetti-Spaccamela
• Rebecca Reiffenhäuser

Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important measure is the adaptive complexity, which captures the number of sequential rounds of parallel computation needed by an algorithm to terminate. In this work, we obtain the first constant factor approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with near-optimal O(log n) adaptive complexity. Low adaptivity by itself, however, is not enough: a crucial feature to account for is represented by the total number of function evaluations (or value queries). Our algorithm asks O ˜ ( n 2 ) value queries but can be modified to run with only O ˜ ( n ), while retaining a low adaptive complexity of O(log2 n). Besides the above improvement in adaptivity, this is also the first combinatorial approach with sublinear adaptive complexity for the problem and yields algorithms comparable to the state-of-the-art even for the special cases of cardinality constraints or monotone objectives.

AAMAS Conference 2025 Conference Paper

Algorithmically Fair Maximization of Multiple Submodular Objective Functions

• Georgios Amanatidis
• Georgios Birmpas
• Philip Lazos
• Stefano Leonardi
• Rebecca Reiffenhäuser

Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such a setting, where the different solutions must be disjoint, and thus, questions of algorithmic fairness arise. Inspired from the fair division literature, we suggest a simple round-robin protocol, where agents are allowed to build their solutions one item at a time by taking turns. Unlike what is typical in fair division, however, the prime goal here is to provide a fair algorithmic environment; each agent is allowed to use any algorithm for constructing their respective solutions. We show that just by following simple greedy policies, agents have solid guarantees for both monotone and non-monotone objectives, and for combinatorial constraints as general as 𝑝-systems (which capture cardinality and matroid intersection constraints). In the monotone case, our results include the first approximate EF1-type guarantees under such general constraints. Further, although following a greedy policy may not be generally optimal, we show that consistently performing better than that is computationally hard.

TIST Journal 2024 Journal Article

Fair Projections as a Means toward Balanced Recommendations

• Aris Anagnostopoulos
• Luca Becchetti
• Matteo Böhm
• Adriano Fazzone
• Stefano Leonardi
• Cristina Menghini
• Chris Schwiegelshohn

The goal of recommender systems is to provide to users suggestions that match their interests, with the eventual goal of increasing their satisfaction, as measured by the number of transactions (clicks, purchases, and so forth). Often, this leads to providing recommendations that are of a particular type. For some contexts (e.g., browsing videos for information) this may be undesirable, as it may enforce the creation of filter bubbles. This is because of the existence of underlying bias in the input data of prior user actions. Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. In this article, we consider both the densest subgraph and the \(k\) -clustering problem, two primitives that are being used by some recommender systems. We are given a coloring on the nodes, respectively the points, and aim to compute a fair solution \(S\), consisting of a subgraph or a clustering, such that none of the colors is disparately impacted by the solution. Unfortunately, introducing fair solutions typically makes these problems substantially more difficult. Unlike the unconstrained densest subgraph problem, which is solvable in polynomial time, the fair densest subgraph problem is NP-hard even to approximate, which means that with the standard computational model it is probably impossible to solve (or even approximate it sufficiently well) in polynomial time. For \(k\) -clustering, the fairness constraints make the problem very similar to capacitated clustering, which is a notoriously hard problem to even approximate. Despite such negative premises, we are able to provide positive results in important use cases. In particular, we are able to prove that a suitable spectral embedding allows recovery of an almost optimal, fair, dense subgraph hidden in the input data, whenever one is present, a result that is further supported by experimental evidence. We also show a polynomial-time, \(2\) -approximation algorithm to the problem of fair densest subgraph, assuming that there exist only two colors and both colors occur equally often in the graph. This result turns out to be optimal assuming the small set expansion hypothesis. For fair \(k\) -clustering, we show that we can recover high quality fair clusterings effectively and efficiently. For the special case of \(k\) -median and \(k\) -center, we offer additional, fast and simple approximation algorithms as well as new hardness results. The above theoretical findings drive the design of heuristics, which we experimentally evaluate on a scenario based on real data, in which our aim is to strike a good balance between diversity and highly correlated items from Amazon co-purchasing graphs and Facebook contacts. We additionally evaluated our algorithmic solutions for the fair \(k\) -median problem through experiments on various real-world datasets.

NeurIPS Conference 2024 Conference Paper

Online Learning with Sublinear Best-Action Queries

• Matteo Russo
• Andrea Celli
• Riccardo Colini-Baldeschi
• Federico Fusco
• Daniel Haimovich
• Dima Karamshuk
• Stefano Leonardi
• Niek Tax

In online learning, a decision maker repeatedly selects one of a set of actions, with the goal of minimizing the overall loss incurred. Following the recent line of research on algorithms endowed with additional predictive features, we revisit this problem by allowing the decision maker to acquire additional information on the actions to be selected. In particular, we study the power of \emph{best-action queries}, which reveal beforehand the identity of the best action at a given time step. In practice, predictive features may be expensive, so we allow the decision maker to issue at most $k$ such queries. We establish tight bounds on the performance any algorithm can achieve when given access to $k$ best-action queries for different types of feedback models. In particular, we prove that in the full feedback model, $k$ queries are enough to achieve an optimal regret of $\Theta(\min\{\sqrt T, \frac{T}{k}\})$. This finding highlights the significant multiplicative advantage in the regret rate achievable with even a modest (sublinear) number $k \in \Omega(\sqrt{T})$ of queries. Additionally, we study the challenging setting in which the only available feedback is obtained during the time steps corresponding to the $k$ best-action queries. There, we provide a tight regret rate of $\Theta(\min\{\frac{T}{\sqrt k}, \frac{T^2}{k^2}\})$, which improves over the standard $\Theta(\frac{T}{\sqrt k})$ regret rate for label efficient prediction for $k \in \Omega(T^{2/3})$.

JMLR Journal 2024 Journal Article

Regret Analysis of Bilateral Trade with a Smoothed Adversary

• Nicolò Cesa-Bianchi
• Tommaso Cesari
• Roberto Colomboni
• Federico Fusco
• Stefano Leonardi

We study repeated bilateral trade where an adaptive $\sigma$-smooth adversary generates the valuations of sellers and buyers. We completely characterize the regret regimes for fixed-price mechanisms under different feedback models in the two cases where the learner can post the same or different prices to buyers and sellers. We begin by showing that, in the full-feedback scenario, the minimax regret after $T$ rounds is of order $\sqrt{T}$. Under partial feedback, any algorithm that has to post the same price to buyers and sellers suffers worst-case linear regret. However, when the learner can post two different prices at each round, we design an algorithm enjoying regret of order $T^{3/4}$, ignoring log factors. We prove that this rate is optimal by presenting a surprising $T^{3/4}$ lower bound, which is the paper's main technical contribution. [abs] [ pdf ][ bib ] &copy JMLR 2024. ( edit, beta )

AAAI Conference 2023 Conference Paper

Fully Dynamic Online Selection through Online Contention Resolution Schemes

• Vashist Avadhanula
• Andrea Celli
• Riccardo Colini-Baldeschi
• Stefano Leonardi
• Matteo Russo

We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial constraints. In the classical ``incremental'' version of the problem, selected elements remain active until the end of the input sequence. On the other hand, in the fully dynamic version of the problem, elements stay active for a limited time interval, and then leave. This models, for example, the online matching of tasks to workers with task/worker-dependent working times, and sequential posted pricing of perishable goods. A successful approach to online selection problems in the adversarial setting is given by the notion of Online Contention Resolution Scheme (OCRS), that uses a priori information to formulate a linear relaxation of the underlying optimization problem, whose optimal fractional solution is rounded online for any adversarial order of the input sequence. Our main contribution is providing a general method for constructing an OCRS for fully dynamic online selection problems. Then, we show how to employ such OCRS to construct no-regret algorithms in a partial information model with semi-bandit feedback and adversarial inputs.

IJCAI Conference 2022 Conference Paper

Fair Equilibria in Sponsored Search Auctions: The Advertisers’ Perspective

• Georgios Birmpas
• Andrea Celli
• Riccardo Colini-Baldeschi
• Stefano Leonardi

In this work we introduce a new class of mechanisms composed of a traditional Generalized Second Price (GSP) auction, and a fair division scheme in order to achieve some desired level of fairness between groups of Bayesian strategic advertisers. We propose two mechanisms, beta-Fair GSP and GSP-EFX, that compose GSP with, respectively, an envy-free up to one item, and an envy-free up to any item fair division scheme. The payments of GSP are adjusted in order to compensate advertisers that suffer a loss of efficiency due the fair division stage. We investigate the strategic learning implications of the deployment of sponsored search auction mechanisms that obey to such fairness criteria. We prove that, for both mechanisms, if bidders play so as to minimize their external regret they are guaranteed to reach an equilibrium with good social welfare. We also prove that the mechanisms are budget balanced, so that the payments charged by the traditional GSP mechanism are a good proxy of the total compensation offered to the advertisers. Finally, we evaluate the quality of the allocations through experiments on real-world data.

JAIR Journal 2022 Journal Article

Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint

• Georgios Amanatidis
• Federico Fusco
• Philip Lazos
• Stefano Leonardi
• Rebecca Reiffenhäuser

Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern-day applications can render existing algorithms prohibitively slow. Moreover, frequently those instances are also inherently stochastic. Focusing on these challenges, we revisit the classic problem of maximizing a (possibly non-monotone) submodular function subject to a knapsack constraint. We present a simple randomized greedy algorithm that achieves a 5.83-approximation and runs in O(n log n) time, i.e., at least a factor n faster than other state-of-the-art algorithms. The versatility of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a (9 + ε)-approximation to the best adaptive policy, which is the first constant approximation for non-monotone objectives. Experimental evaluation of our algorithms showcases their improved performance on real and synthetic data.

NeurIPS Conference 2020 Conference Paper

Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint

• Georgios Amanatidis
• Federico Fusco
• Philip Lazos
• Stefano Leonardi
• Rebecca Reiffenhäuser

Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern-day applications can render existing algorithms prohibitively slow. Moreover, frequently those instances are also inherently stochastic. Focusing on these challenges, we revisit the classic problem of maximizing a (possibly non-monotone) submodular function subject to a knapsack constraint. We present a simple randomized greedy algorithm that achieves a $5. 83$ approximation and runs in $O(n \log n)$ time, i. e. , at least a factor $n$ faster than other state-of-the-art algorithms. The robustness of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a 9-approximation to the best adaptive policy, which is the first constant approximation for non-monotone objectives. Experimental evaluation of our algorithms showcases their improved performance on real and synthetic data.

TCS Journal 2020 Journal Article

FUN editorial

• Hiro Ito
• Stefano Leonardi
• Linda Pagli
• Giuseppe Prencipe

IJCAI Conference 2020 Conference Paper

Online Revenue Maximization for Server Pricing

• Shant Boodaghians
• Federico Fusco
• Stefano Leonardi
• Yishay Mansour
• Ruta Mehta

Efficient and truthful mechanisms to price time on remote servers/machines have been the subject of much work in recent years due to the importance of the cloud market. This paper considers online revenue maximization for a unit capacity server, when jobs are non preemptive, in the Bayesian setting: at each time step, one job arrives, with parameters drawn from an underlying distribution. We design an efficiently computable truthful posted price mechanism, which maximizes revenue in expectation and in retrospect, up to additive error. The prices are posted prior to learning the agent's type, and the computed pricing scheme is deterministic. We also show the pricing mechanism is robust to learning the job distribution from samples, where polynomially many samples suffice to obtain near optimal prices.

TCS Journal 2020 Journal Article

Prior-free multi-unit auctions with ordered bidders

• Sayan Bhattacharya
• Elias Koutsoupias
• Janardhan Kulkarni
• Stefano Leonardi
• Tim Roughgarden
• Xiaoming Xu

Prior-free auctions are robust auctions that assume no distribution over bidders' valuations and provide worst-case (input-by-input) approximation guarantees. In contrast to previous work on this topic, we pursue good prior-free auctions with non-identical bidders. Prior-free auctions can approximate meaningful benchmarks for non-identical bidders only when sufficient qualitative information about the bidder asymmetry is publicly known. We consider digital goods auctions where there is a total ordering of the bidders that is known to the seller, where earlier bidders are in some sense thought to have higher valuations. We use the framework of Hartline and Roughgarden (STOC'08) to define an appropriate revenue benchmark: the maximum revenue that can be obtained from a bid vector using prices that are nonincreasing in the bidder ordering and bounded above by the second-highest bid. This monotone-price benchmark is always as large as the well-known fixed-price benchmark F ( 2 ), so designing prior-free auctions with good approximation guarantees is only harder. By design, an auction that approximates the monotone-price benchmark satisfies a very strong guarantee: it is, in particular, simultaneously near-optimal for essentially every Bayesian environment in which bidders' valuation distributions have nonincreasing monopoly prices, or in which the distribution of each bidder stochastically dominates that of the next. Even when there is no distribution over bidders' valuations, such an auction still provides a quantifiable input-by-input performance guarantee. In this paper, we design a simple O ( 1 ) -competitive prior-free auction for digital goods with ordered bidders. We also extend the monotone-price benchmark and our O ( 1 ) -competitive prior-free auction to multi-unit settings with limited supply.

NeurIPS Conference 2016 Conference Paper

Community Detection on Evolving Graphs

• Aris Anagnostopoulos
• Jakub Łącki
• Silvio Lattanzi
• Stefano Leonardi
• Mohammad Mahdian

Clustering is a fundamental step in many information-retrieval and data-mining applications. Detecting clusters in graphs is also a key tool for finding the community structure in social and behavioral networks. In many of these applications, the input graph evolves over time in a continual and decentralized manner, and, to maintain a good clustering, the clustering algorithm needs to repeatedly probe the graph. Furthermore, there are often limitations on the frequency of such probes, either imposed explicitly by the online platform (e. g. , in the case of crawling proprietary social networks like twitter) or implicitly because of resource limitations (e. g. , in the case of crawling the web). In this paper, we study a model of clustering on evolving graphs that captures this aspect of the problem. Our model is based on the classical stochastic block model, which has been used to assess rigorously the quality of various static clustering methods. In our model, the algorithm is supposed to reconstruct the planted clustering, given the ability to query for small pieces of local information about the graph, at a limited rate. We design and analyze clustering algorithms that work in this model, and show asymptotically tight upper and lower bounds on their accuracy. Finally, we perform simulations, which demonstrate that our main asymptotic results hold true also in practice.

TCS Journal 2013 Journal Article

Preface

• Camil Demetrescu
• Stefano Leonardi
• Alberto Marchetti-Spaccamela

TCS Journal 2012 Journal Article

Game-theoretic analysis of Internet switching with selfish users

• Alex Kesselman
• Stefano Leonardi

We consider the problem of Internet switching, where traffic is generated by selfish users. We study a packetized (TCP-like) traffic model, which is more accurate than the widely used fluid model. We assume that routers have First-In-First-Out (FIFO) buffers of bounded capacity managed by the drop-tail policy. The utility of each user depends on its goodput and the congestion level. Since selfish users try to maximize their own utility disregarding the system objectives, we study Nash equilibria that correspond to a steady state of the system. We quantify the degradation in the network performance called the price of anarchy resulting from such selfish behavior. We show that for a single bottleneck buffer, the price of anarchy is proportional to the number of users. Then we propose a simple modification of the Random Early Detection (RED) drop policy, which reduces the price of anarchy to a constant. We demonstrate that a Nash equilibrium can be reached if all users deploy TCP Vegas as their transport protocol under the drop-tail policy. We also consider some natural extensions of our model including the case of multiple Quality of Service (QoS) requirements, routing on parallel links and general networks with multiple bottlenecks.

TCS Journal 2004 Journal Article

Cross-monotonic cost sharing methods for connected facility location games

• Stefano Leonardi
• Guido Schäfer

We present cost sharing methods for connected facility location games that are cross-monotonic and competitive and that recover a constant fraction of the cost of the constructed solution. The novelty of this paper is that we use randomized algorithms and that we share the expected cost among the participating users. As a consequence, our cost sharing methods are simple and achieve attractive approximation ratios. We also provide a primal-dual cost sharing method for the connected facility location game with opening costs.

TCS Journal 2004 Journal Article

Semi-clairvoyant scheduling

• Luca Becchetti
• Stefano Leonardi
• Alberto Marchetti-Spaccamela
• Kirk Pruhs

In (Symp. Discrete Algorithms 2002, p. 762) it was shown that the obvious semi-clairvoyant generalization of the Shortest Processing Time is O(1)-competitive with respect to average stretch on a single machine. In (Symp. Discrete Algorithms 2002, p. 762) it was left as an open question whether it was possible for a semi-clairvoyant algorithm to be O(1)-competitive with respect to average flow time on a single machine. Here we settle this open question by giving a semi-clairvoyant algorithm that is O(1)-competitive with respect to average flow time on a single machine. We also show a semi-clairvoyant algorithm on parallel machines that achieves up to constant factors the best known competitive ratio for clairvoyant on-line algorithms. In some sense one might conclude from this that the QoS achievable by semi-clairvoyant algorithms is competitive with clairvoyant algorithms. We finally show that, in contrast to the clairvoyant case, no semi-clairvoyant algorithm can be simultaneously O(1)-competitive with respect to average stretch and O(1)-competitive with respect to average flow time.

TCS Journal 2001 Journal Article

Preface

• Stefano Leonardi
• Alberto Marchetti-Spaccamela

TCS Journal 1999 Journal Article

Ondashline routing in all-optical networks

• Yair Bartal
• Stefano Leonardi

The paper deals with ondashline routing in wavelength division multiplexing (WDM) optical networks. A sequence of requests arrives over time, each is a pair of nodes to be connected by a path. The problem is to assign a wavelength and a path to each pair, so that no two paths sharing a link are assigned the same wavelength. The goal is to minimize the number of wavelengths used to establish all connections. Raghavan and Upfal (Proc. 26th Annual Symp. on Theory of Computing, 1994, pp. 133–143) considered the off-line version of the problem, which was further studied in Aumann and Rabani (Proc. 6th ACM-SIAM Symp. on Discrete Algorithms, 1995, pp. 567–576), Kaklamanis and Persiano (Proc. 4th Annual European Symp. on Algorithms, Lecture Notes in Computer Science, vol. 1136, Springer, Berlin, 1996, pp. 460–470), Mihail et al. (Proc. 36th IEEE Annual Symp. on Foundations of Computer Science, 1995, pp. 548–557), Rabani, (Proc. 37th Annual Symp. on Foundations of Computer Science, 1996, pp. 400–409). For a line topology, the problem is the well-studied interval graph coloring problem. Ondashline algorithms for this problem have been analyzed in Kierstead and Trotter (Congr. Numer. 33 (1981) 143–153). We consider trees, trees of rings, and meshes topologies, previously studied in the off-line case. We give ondashline algorithms with competitive ratio O(log n) for all these topologies. We give a matching Ω(log n) lower bound for meshes. We also prove that any algorithm for trees cannot have competitive ratio better than Ω(log n/log log n). We also consider the problem where every edge is associated with parallel links. While in WDM technology, a fiber link requires different wavelengths for every transmission, space division multiplexing technology allows parallel links for a single wavelength, at an additional cost. Thus, it may be beneficial in terms of network economics to combine between the two technologies (this is indeed done in practice). For arbitrary networks with Ω(log n) parallel links we give an ondashline algorithm with competitive ratio O(log n).