arXiv subjects

Dimitris Fotakis

Publications and source records attributed to Dimitris Fotakis.

At least 19 recordsLinked to original sources

arXiv2026

Leveraging Recourse and Size Bounds for OnlineKnapsack with Removable Items

In the online unweighted knapsack problem, items arrive sequentially and must be accepted or rejected immediately for a bounded-capacity knapsack, aiming to maximize the total size of accepted items. When decisions are irrevocable, no algorithm achieves a non-trivial competitive ratio. An essential relaxation that circumvents this impossibility is to allow previously accepted items to be removed from the knapsack (a.k.a. removal). In this work, we investigate possible further improvements on the competitive ratio with removal by bringing together two other previously proposed model extensions: knowledge of an upper bound on the item sizes (a.k.a. bound awareness) and ability to reinsert previously rejected items(a.k.a.recourse). Our contributions are twofold. First, we establish close upper and lower bounds on the competitive ratio under bound awareness, removal and recourse. We show that significant improvements on the best known competitive ratio are possible when the upper bound on the item sizes is not too restrictive and only few uses of recourse are available. Second, we introduce the notion of adaptive online algorithms which do not require to know any upper bound on the item sizes but still achieve performance guarantees comparable to the ones obtained under the bound awareness model.

cs.DS↗

arXiv2026

A Nearly Tight Lower Bound for Matroid Intersection Prophet Inequalities

We study prophet inequalities under intersections of $q$ partition matroids, where an online algorithm irrevocably selects elements with independent nonnegative values drawn from known distributions and revealed in an adversarial order. We prove an $Ω(q/\log q)$ lower bound on the competitive ratio. Together with the known $O(q)$ upper bounds, this resolves, up to a logarithmic factor, the optimal dependence on $q$, an open question posed by Correa, Cristi, Fielbaum, Pollner, and Weinberg (IPCO 2022) and Saxena, Velusamy, and Weinberg (ITCS 2023). Our construction also yields an $Ω(d/\log d)$ lower bound for $d$-single-minded auctions, where buyers request fixed bundles of at most $d$ unit-capacity items. Our construction and analysis build on the big-decisions-first framework of Rubinstein and Singla (STOC 2026). Previous lower bounds for this problem hold even for i.i.d. Bernoulli values, whereas our instance uses nonidentical distributions. For i.i.d. Bernoulli values, we prove a $q^{1-o(1)}$ lower bound, improving the previous $q^{1/2+Ω(1/\log\log q)}$ of Saxena, Velusamy, and Weinber (ITCS 2023). To this end, we construct $p^p$ pairwise qualitatively independent partitions into $p$ blocks on a ground set of only $p^{2+o(1)}$ points.

cs.GT↗

arXiv2026

FAIR-Compute: A Roadmap for Fair and Efficient Allocation of Federated Digital Research Infrastructure

As demand for high-performance computing (HPC), high-throughput computing and data storage grows, the way scarce compute is allocated -- not just how much exists -- has become a decisive factor in the productivity of UK research. FAIR-Compute studies allocation in a federated Digital Research Infrastructure (DRI) as a problem at the intersection of algorithmic game theory, transport economics and HPC scheduling. Our central observation is simple: once a shared system must decide who runs, when and under what evidence, its scheduler settings cease to be a purely technical matter and become policy. The project combined three strands of evidence: a landscape review of UK and international allocation practice (including EuroHPC, WLCG, ACCESS, JASMIN and DiRAC) supported by a stakeholder survey; a mechanism-design model of allocation under strategic and uncertain user reports; and a simulation study built on the public Fresco/Anvil workload trace and controlled synthetic stress tests. Three results recur across all three strands. First, allocation records measure occupancy (resources reserved) rather than utilisation (useful work done), so the system cannot currently answer the question UKRI and DSIT most want answered -- whether resources deliver productive value. Second, simple, transparent scheduling heuristics perform close to an offline full-information benchmark once tuned, so the near-term opportunity is to tune and instrument existing schedulers rather than replace them. Third, federation is genuinely valuable but behaves like uncoordinated routing when left unmanaged: it can minimise average delay while quietly concentrating load -- and potentially harm -- on the receiving system. This mirrors a classic effect from road-traffic economics (Braess's paradox), where letting everyone independently pick the fastest route can leave the whole network worse off.

cs.DC↗

arXiv2026

The Knapsack Secretary Problem is Strictly Harder Than the Secretary Problem

The knapsack secretary problem is a generalization of the classical secretary problem where the accepted items must satisfy a knapsack constraint. A line of work has developed constant-competitive algorithms for this problem, with successive improvements culminating in the current best-known competitive ratio of $0.153$. A natural open question was whether the optimal $1/e$ competitive ratio for the classical secretary problem is also achievable for the knapsack secretary problem. We answer this question negatively by showing that no $(1/e - 0.0001)$-competitive algorithm exists for the knapsack secretary problem. The analysis of the family of hard instances we construct proceeds in three steps. First, we reduce the cardinal problem on these instances to an almost-ordinal problem. Second, we formulate a linear program that captures the performance of almost-ordinal algorithms on this instance family. Finally, we exhibit a feasible dual solution whose objective value is strictly below $1/e$. We also give an algorithm that improves the best-known competitive ratio from $0.153$ to $0.178$.

cs.DS↗

arXiv2026

A Unified Framework for Uniform-Price Resource Allocation Mechanisms

Mechanisms for allocating a divisible resource among strategic agents have been widely studied. The prominent paradigm is the proportional (Kelly) mechanism, which elicits a scalar bid per agent, allocates the resource proportionally, and charges payments equal to the bids. Follow-up mechanisms improve social welfare, but sacrifice simplicity by introducing complex allocation rules or unintuitive payments. We introduce a unified framework for designing simple resource allocation mechanisms with proportional-style allocations and uniform pricing. Our framework yields a family of mechanisms that interpolate between the Kelly mechanism and the first-price auction. These mechanisms strictly improve upon Kelly's efficiency guarantees, even achieving full efficiency in equilibrium, while also providing revenue guarantees relative to the VCG mechanism.

cs.GT↗

arXiv2026

Repeated Descent: A Framework for Online Budget-Feasible Auctions

We study budget feasible procurement auctions, in which $n$ agents, each with a privately held service cost, offer their services to an employer. The employer seeks to maximize a public submodular valuation function over the set of hired agents, while facing a hard budget constraint. We consider an online posted-price setting, in which agents arrive in a uniformly random order (a.k.a. \emph{secretary arrivals}) and the employer must make irrevocable take-it-or-leave-it offers upon their arrival. The employer does not get any feedback about the agent service costs other than whether they accept the offer or not. We introduce Repeated Descent (a.k.a. \RED), a deterministic framework based on adaptive linear posted pricing. \RED enforces budget feasibility by adaptively adjusting its pricing and balancing each pricing level with the number of agents considered in it. Using \RED as the main building block, we obtain a $1046$-competitive posted-price mechanism for online budget feasible auctions with secretary agent arrivals and submodular valuations, thus improving on the previously best known ratio of (Charalampopoulos et al., EC 2025) by several orders of magnitude. Combining \RED with random subsampling, we obtain the first constant-competitive posted-price budget feasible mechanism for non-monotone submodular valuations. On the negative side, we show that every online budget feasible mechanism with XOS valuations has a competitive ratio of $Ω\!\left(\tfrac{\log n}{(\log\log n)^2}\right)$.

cs.GT↗

arXiv2026

Efficient Parameter Estimation of Truncated Boolean Product Distributions

We study the problem of estimating the parameters of a Boolean product distribution in $d$ dimensions, when the samples are truncated by a set $S \subset \{0, 1\}^d$ accessible through a membership oracle. This is the first time that the computational and statistical complexity of learning from truncated samples is considered in a discrete setting. We introduce a natural notion of fatness of the truncation set $S$, under which truncated samples reveal enough information about the true distribution. We show that if the truncation set is sufficiently fat, samples from the true distribution can be generated from truncated samples. A stunning consequence is that virtually any statistical task (e.g., learning in total variation distance, parameter estimation, uniformity or identity testing) that can be performed efficiently for Boolean product distributions, can also be performed from truncated samples, with a small increase in sample complexity. We generalize our approach to ranking distributions over $d$ alternatives, where we show how fatness implies efficient parameter estimation of Mallows models from truncated samples. Exploring the limits of learning discrete models from truncated samples, we identify three natural conditions that are necessary for efficient identifiability: (i) the truncation set $S$ should be rich enough; (ii) $S$ should be accessible through membership queries; and (iii) the truncation by $S$ should leave enough randomness in all directions. By carefully adapting the Stochastic Gradient Descent approach of (Daskalakis et al., FOCS 2018), we show that these conditions are also sufficient for efficient learning of truncated Boolean product distributions.

cs.LG↗

arXiv2026

Online Resource Allocation via Static Bundle Pricing

Online Resource Allocation addresses the problem of efficiently allocating limited resources to buyers with incomplete knowledge of future requests. In our setting, buyers arrive sequentially requesting a set of items, each with a value drawn from a known distribution. We study the efficiency of static and anonymous bundle pricing in environments where the buyers' valuations exhibit strong complementarities. In such settings, standard item pricing fails to leverage item multiplicities, while static bundle pricing mechanisms are only known for very restricted domains and their analysis relies on domain-specific arguments. We develop a unified bundle pricing framework for online resource allocation in three well-studied domains with complementarities: (i) single-minded combinatorial auctions with maximum bundle size $d$; (ii) general single-minded combinatorial auctions; and (iii) network routing, where each buyer aims to route a unit of flow from a source node $s$ to a target node $t$ in a capacitated network. Our approach yields static and anonymous bundle pricing mechanisms whose performance improves exponentially with item multiplicity. For the $d$-single-minded setting with minimum item multiplicity $B$, we obtain an $O(d^{1/B})$-competitive mechanism. For general single-minded combinatorial auctions and online network routing, we obtain $O(m^{1/(B+1)})$-competitive mechanisms, where $m$ is the number of items. We complement these results with information-theoretic lower bounds. We show that no online algorithm can achieve a competitive ratio better than $ \widetildeΩ(m^{1/(B+2)})$ for single-minded combinatorial auctions and $ \widetildeΩ(d^{1/(B+1)})$ for the $d$-single-minded setting. Our constructions exploit a deep connection to the extremal combinatorics problem of determining the maximum number of qualitatively independent partitions of a ground set.

cs.GT↗

arXiv2025

GLANCE: Global Actions in a Nutshell for Counterfactual Explainability

The widespread deployment of machine learning systems in critical real-world decision-making applications has highlighted the urgent need for counterfactual explainability methods that operate effectively. Global counterfactual explanations, expressed as actions to offer recourse, aim to provide succinct explanations and insights applicable to large population subgroups. High effectiveness, measured by the fraction of the population that is provided recourse, ensures that the actions benefit as many individuals as possible. Keeping the cost of actions low ensures the proposed recourse actions remain practical and actionable. Limiting the number of actions that provide global counterfactuals is essential to maximizing interpretability. The primary challenge, therefore, is to balance these trade-offs--maximizing effectiveness, minimizing cost, while maintaining a small number of actions. We introduce $\texttt{GLANCE}$, a versatile and adaptive algorithm that employs a novel agglomerative approach, jointly considering both the feature space and the space of counterfactual actions, thereby accounting for the distribution of points in a way that aligns with the model's structure. This design enables the careful balancing of the trade-offs among the three key objectives, with the size objective functioning as a tunable parameter to keep the actions few and easy to interpret. Our extensive experimental evaluation demonstrates that $\texttt{GLANCE}$ consistently shows greater robustness and performance compared to existing methods across various datasets and models.

cs.LG↗

arXiv2025

Analyzing the Effect of Embedding Norms and Singular Values to Oversmoothing in Graph Neural Networks

In this paper, we study the factors that contribute to the effect of oversmoothing in deep Graph Neural Networks (GNNs). Specifically, our analysis is based on a new metric (Mean Average Squared Distance - $MASED$) to quantify the extent of oversmoothing. We derive layer-wise bounds on $MASED$, which aggregate to yield global upper and lower distance bounds. Based on this quantification of oversmoothing, we further analyze the importance of two different properties of the model; namely the norms of the generated node embeddings, along with the largest and smallest singular values of the weight matrices. Building on the insights drawn from the theoretical analysis, we show that oversmoothing increases as the number of trainable weight matrices and the number of adjacency matrices increases. We also use the derived layer-wise bounds on $MASED$ to form a proposal for decoupling the number of hops (i.e., adjacency depth) from the number of weight matrices. In particular, we introduce G-Reg, a regularization scheme that increases the bounds, and demonstrate through extensive experiments that by doing so node classification accuracy increases, achieving robustness at large depths. We further show that by reducing oversmoothing in deep networks, we can achieve better results in some tasks than using shallow ones. Specifically, we experiment with a ``cold start" scenario, i.e., when there is no feature information for the unlabeled nodes. Finally, we show empirically the trade-off between receptive field size (i.e., number of weight matrices) and performance, using the $MASED$ bounds. This is achieved by distributing adjacency hops across a small number of trainable layers, avoiding the extremes of under- or over-parameterization of the GNN.

cs.LG↗

arXiv2025

A Competitive Posted-Price Mechanism for Online Budget-Feasible Auctions

We consider online procurement auctions, where the agents arrive sequentially, in random order, and have private costs for their services. The buyer aims to maximize a monotone submodular value function for the subset of agents whose services are procured, subject to a budget constraint on their payments. We consider a posted-price setting where upon each agent's arrival, the buyer decides on a payment offered to them. The agent accepts or rejects the offer, depending on whether the payment exceeds their cost, without revealing any other information about their private costs whatsoever. We present a randomized online posted-price mechanism with constant competitive ratio, thus resolving the main open question of (Badanidiyuru, Kleinberg and Singer, EC 2012). Posted-price mechanisms for online procurement typically operate by learning an estimation of the optimal value, denoted as OPT, and using it to determine the payments offered to the agents. The main challenge is to learn OPT within a constant factor from the agents' accept / reject responses to the payments offered. Our approach is based on an online test of whether our estimation is too low compared against OPT and a carefully designed adaptive search that gradually refines our estimation.

cs.GT↗

arXiv2025

A Query-Driven Approach to Space-Efficient Range Searching

We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle, and must be selected such that it optimizes a meaningful performance parameter on expectation. Our first contribution is to show that a near-linear sample of queries allows the construction of a partition tree with a near-optimal expected number of nodes visited during querying. We enhance this approach by treating node processing as a classification problem, leveraging fast classifiers like shallow neural networks to obtain experimentally efficient query times. Our second contribution is to develop partition trees using sparse geometric separators. Our preprocessing algorithm, based on a sample of queries, builds a balanced tree with nodes associated with separators that minimize query stabs on expectation; this yields both fast processing of each node and a small number of visited nodes, significantly reducing query time.

cs.DS↗

arXiv2025

Polynomial Time Learning-Augmented Algorithms for NP-hard Permutation Problems

We consider a learning-augmented framework for NP-hard permutation problems. The algorithm has access to predictions telling, given a pair $u,v$ of elements, whether $u$ is before $v$ or not in an optimal solution. Building on the work of Braverman and Mossel (SODA 2008), we show that for a class of optimization problems including scheduling, network design and other graph permutation problems, these predictions allow to solve them in polynomial time with high probability, provided that predictions are true with probability at least $1/2+ε$. Moreover, this can be achieved with a parsimonious access to the predictions.

cs.DS↗

arXiv2024

Reducing Oversmoothing through Informed Weight Initialization in Graph Neural Networks

In this work, we generalize the ideas of Kaiming initialization to Graph Neural Networks (GNNs) and propose a new scheme (G-Init) that reduces oversmoothing, leading to very good results in node and graph classification tasks. GNNs are commonly initialized using methods designed for other types of Neural Networks, overlooking the underlying graph topology. We analyze theoretically the variance of signals flowing forward and gradients flowing backward in the class of convolutional GNNs. We then simplify our analysis to the case of the GCN and propose a new initialization method. Our results indicate that the new method (G-Init) reduces oversmoothing in deep GNNs, facilitating their effective use. Experimental validation supports our theoretical findings, demonstrating the advantages of deep networks in scenarios with no feature information for unlabeled nodes (i.e., ``cold start'' scenario).

cs.LG↗

arXiv2024

Partially Trained Graph Convolutional Networks Resist Oversmoothing

In this work we investigate an observation made by Kipf \& Welling, who suggested that untrained GCNs can generate meaningful node embeddings. In particular, we investigate the effect of training only a single layer of a GCN, while keeping the rest of the layers frozen. We propose a basis on which the effect of the untrained layers and their contribution to the generation of embeddings can be predicted. Moreover, we show that network width influences the dissimilarity of node embeddings produced after the initial node features pass through the untrained part of the model. Additionally, we establish a connection between partially trained GCNs and oversmoothing, showing that they are capable of reducing it. We verify our theoretical results experimentally and show the benefits of using deep networks that resist oversmoothing, in a ``cold start'' scenario, where there is a lack of feature information for unlabeled nodes.

cs.LG↗

arXiv2024

On the Distortion of Committee Election with 1-Euclidean Preferences and Few Distance Queries

We consider committee election of $k \geq 2$ (out of $m \geq k+1$) candidates, where the voters and the candidates are associated with locations on the real line. Each voter's cardinal preferences over candidates correspond to her distance to the candidate locations, and each voter's cardinal preferences over committees is defined as her distance to the nearest candidate elected in the committee. We consider a setting where the true distances and the locations are unknown. We can nevertheless have access to degraded information which consists of an order of candidates for each voter. We investigate the best possible distortion (a worst-case performance criterion) wrt. the social cost achieved by deterministic committee election rules based on ordinal preferences submitted by $n$ voters and few additional distance queries. For $k = 2$, we achieve bounded distortion without any distance queries; we show that the distortion is $3$ for $m = 3$, and that the best possible distortion achieved by deterministic algorithms is at least $n-1$ and at most $n+1$, for any $m \geq 4$. For any $k \geq 3$, we show that the best possible distortion of any deterministic algorithm that uses at most $k-3$ distance queries cannot be bounded by any function of $n$, $m$ and $k$. We present deterministic algorithms for $k$-committee election with distortion of $O(n)$ with $O(k)$ distance queries and $O(1)$ with $O(k \log n)$ distance queries.

cs.GT↗

arXiv2024

Improved Bounds for Online Facility Location with Predictions

We consider Online Facility Location in the framework of learning-augmented online algorithms. In Online Facility Location (OFL), demands arrive one-by-one in a metric space and must be (irrevocably) assigned to an open facility upon arrival, without any knowledge about future demands. We focus on uniform facility opening costs and present an online algorithm for OFL that exploits potentially imperfect predictions on the locations of the optimal facilities. We prove that the competitive ratio decreases from sublogarithmic in the number of demands $n$ to constant as the so-called $η_1$ error, i.e., the sum of distances of the predicted locations to the optimal facility locations, decreases. E.g., our analysis implies that if for some $\varepsilon > 0$, $η_1 = \mathrm{OPT} / n^\varepsilon$, where $\mathrm{OPT}$ is the cost of the optimal solution, the competitive ratio becomes $O(1/\varepsilon)$. We complement our analysis with a matching lower bound establishing that the dependence of the algorithm's competitive ratio on the $η_1$ error is optimal, up to constant factors. Finally, we evaluate our algorithm on real world data and compare the performance of our learning-augmented approach against the performance of the best known algorithm for OFL without predictions.

cs.DS↗

arXiv2024

Reconstructing the mid-infrared spectra of galaxies using ultraviolet to submillimeter photometry and Deep Generative Networks

The mid-infrared spectra of galaxies are rich in features such as the Polycyclic Aromatic Hydrocarbon (PAH) and silicate dust features which give valuable information about the physics of galaxies and their evolution. For example they can provide information about the relative contribution of star formation and accretion from a supermassive black hole to the power output of galaxies. However, the mid-infrared spectra are currently available for a very small fraction of galaxies that have been detected in deep multi-wavelength surveys of the sky. In this paper we explore whether Deep Generative Network methods can be used to reconstruct mid-infrared spectra in the 5-35μm range using the limited multi-wavelength photometry in ~20 bands from the ultraviolet to the submillimeter which is typically available in extragalactic surveys. For this purpose we use simulated spectra computed with a combination of radiative transfer models for starbursts, active galactic nucleus (AGN) tori and host galaxies. We find that our method using Deep Generative Networks, namely Generative Adversarial Networks and Generative Latent Optimization models, can efficiently produce high quality reconstructions of mid-infrared spectra in ~70% of the cases.

astro-ph.GA↗