arXiv subjects

Ola Svensson

Publications and source records attributed to Ola Svensson.

At least 19 recordsLinked to original sources

arXiv2026

TCS-BENCH: Benchmarking State-of-the-Art Generative AI Theoretical Computer Science Research Ability

We introduce TCS-Bench, a benchmark for evaluating Large Language Models (LLMs) on research-level Theoretical Computer Science (TCS) proof generation. TCS-Bench consists of theorem-proving tasks from papers published at top theoretical computer science venues (STOC, FOCS, and SODA). Each task provides the necessary context to derive a self-contained proof for a target result. We evaluate state-of-the-art models on this benchmark. We verify the correctness of generated proofs via a verification agent, and further benchmark the verifier against human-expert proof judgements on a set of target statements and generated proofs pairs. Our reference verifier achieves over 90% accuracy on the expert labeled set.

cs.CL↗

arXiv2026

Space-Efficient Language Generation in the Limit

We initiate a resource-aware theory of \textit{language generation in the limit} under the minimal constraint of space efficiency. In our framework, a learner observes an adversarial positive stream from a target language $K$ and must eventually output a hallucination-free hypothesis language $L \subseteq K$ while omitting at most $Δ$ strings of $K$. We focus on $\mathcal{C}_{s,k}$, the collection of languages recognized by DFAs with at most $s$ states over an alphabet of size $k$, as the natural hypothesis class for memory-bounded learners. In the exponential-space regime, we prove that a learner can exactly identify the target $K$. Under a stricter memory budget, we characterize the strongest possible generation guarantees. In particular, we present a streaming algorithm using $\mathrm{poly}(s,k)$ space that converges to a hypothesis with generation gap $Δ= O(k^{2s-2})$. Moreover, the learned hypothesis captures every string in $K$ of length at least $2s-1$. We complement this result with a near-matching lower bound through a reduction from a standard communication complexity problem. Specifically, achieving generation gap $Δ\le k^{(1-\varepsilon)s}$ requires $k^{Ω(\varepsilon s)}$ memory. Together, these results reveal a sharp transition between polynomial-space generation and exponential-space exact identification.

cs.DS↗

arXiv2026

A General Framework for Dynamic Consistent Submodular Maximization

Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.

cs.DS↗

arXiv2026

Retriever Portfolios: A Principled Approach to Adaptive RAG

Retrieval-augmented generation (RAG) systems typically rely on a single retriever and a single set of hyperparameters, despite facing highly heterogeneous queries that range from simple factoid questions to complex multi-hop reasoning. We propose a method that automatically selects a small, diverse subset of retrievers (a portfolio) from a large pool of candidates, to cover different regions of the target query distribution. We formalize this setting via an expected best-of-$k$ objective over the query distribution and show that it admits an efficient portfolio construction algorithm with near-optimal guarantees. Across multiple QA benchmarks, our learned portfolios and router pipeline consistently outperform single-retriever and naive multi-retriever baselines on both retrieval metrics and answer quality. In addition, compared to inference-time hyperparameter tuning approaches, fixed portfolios enable parallel retrieval and LLM calls, achieving comparable (and sometimes better) accuracy with substantially lower latency and token cost.

cs.LG↗

arXiv2026

A $(2+\varepsilon)$-Approximation Algorithm for Metric $k$-Median

In the classical NP-hard metric $k$-median problem, we are given a set of $n$ clients and centers with metric distances between them, along with an integer parameter $k\geq 1$. The objective is to select a subset of $k$ open centers that minimizes the total distance from each client to its closest open center. In their seminal work, Jain, Mahdian, Markakis, Saberi, and Vazirani presented the Greedy algorithm for facility location, which implies a $2$-approximation algorithm for $k$-median that opens $k$ centers in expectation. Since then, substantial research has aimed at narrowing the gap between their algorithm and the best achievable approximation by an algorithm guaranteed to open exactly $k$ centers. During the last decade, all improvements have been achieved by leveraging their algorithm or a small improvement thereof, followed by a second step called bi-point rounding, which inherently increases the approximation guarantee. Our main result closes this gap: for any $ε>0$, we present a $(2+ε)$-approximation algorithm for $k$-median, improving the previous best-known approximation factor of $2.613$. Our approach builds on a combination of two algorithms. First, we present a non-trivial modification of the Greedy algorithm that operates with $O(\log n/ε^2)$ adaptive phases. Through a novel walk-between-solutions approach, this enables us to construct a $(2+ε)$-approximation algorithm for $k$-median that consistently opens at most $k + O(\log n{/ε^2})$ centers. Second, we develop a novel $(2+ε)$-approximation algorithm tailored for stable instances, where removing any center from an optimal solution increases the cost by at least an $Ω(ε^3/\log n)$ fraction. Achieving this involves a sampling approach inspired by the $k$-means++ algorithm and a reduction to submodular optimization subject to a partition matroid.

cs.DS↗

arXiv2026

A Strong Linear Programming Relaxation for Weighted Tree Augmentation

The Weighted Tree Augmentation Problem (WTAP) is a fundamental network design problem where the goal is to find a minimum-cost set of additional edges (links) to make an input tree 2-edge-connected. While a 2-approximation is standard and the integrality gap of the classic Cut LP relaxation is known to be at least 1.5, achieving approximation factors significantly below 2 has proven challenging. Recent advances of Traub and Zenklusen using local search culminated in a ratio of $1.5+ε$, establishing the state-of-the-art. In this work, we present a randomized approximation algorithm for WTAP with an approximation ratio below 1.49. Our approach is based on designing and rounding a strong linear programming relaxation for WTAP which incorporates variables that represent subsets of edges and the links used to cover them, inspired by lift-and-project methods like Sherali-Adams.

cs.DS↗

arXiv2026

An Optimal Algorithm for Stochastic Vertex Cover

The goal in the stochastic vertex cover problem is to obtain an approximately minimum vertex cover for a graph $G^\star$ that is realized by sampling each edge independently with some probability $p\in (0, 1]$ in a base graph $G = (V, E)$. The algorithm is given the base graph $G$ and the probability $p$ as inputs, but its only access to the realized graph $G^\star$ is through queries on individual edges in $G$ that reveal the existence (or not) of the queried edge in $G^\star$. In this paper, we resolve the central open question for this problem: to find a $(1+\varepsilon)$-approximate vertex cover using only $O_\varepsilon(n/p)$ edge queries. Prior to our work, there were two incomparable state-of-the-art results for this problem: a $(3/2+\varepsilon)$-approximation using $O_\varepsilon(n/p)$ queries (Derakhshan, Durvasula, and Haghtalab, 2023) and a $(1+\varepsilon)$-approximation using $O_\varepsilon((n/p)\cdot \mathrm{RS}(n))$ queries (Derakhshan, Saneian, and Xun, 2025), where $\mathrm{RS}(n)$ is known to be at least $2^{Ω\left(\frac{\log n}{\log \log n}\right)}$ and could be as large as $\frac{n}{2^{Θ(\log^* n)}}$. Our improved upper bound of $O_{\varepsilon}(n/p)$ matches the known lower bound of $Ω(n/p)$ for any constant-factor approximation algorithm for this problem (Behnezhad, Blum, and Derakhshan, 2022). A key tool in our result is a new concentration bound for the size of minimum vertex cover on random graphs, which might be of independent interest.

cs.DS↗

arXiv2026

Accelerating Scientific Research with Gemini: Case Studies and Common Techniques

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

cs.CL↗

arXiv2025

Clustering with Label Consistency

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the real-world need for stable point labels, i.e., stable assignments of points to named sets (clusters). In this paper, we address this gap by initiating the study of label-consistent metric clustering. We first introduce a new notion of consistency, measuring the label distance between two consecutive solutions. Then, armed with this new definition, we design new consistent approximation algorithms for the classical $k$-center and $k$-median problems.

cs.DS↗

arXiv2025

Online Edge Coloring: Sharp Thresholds

Vizing's theorem guarantees that every graph with maximum degree $Δ$ admits an edge coloring using $Δ+ 1$ colors. In online settings - where edges arrive one at a time and must be colored immediately - a simple greedy algorithm uses at most $2Δ- 1$ colors. Over thirty years ago, Bar-Noy, Motwani, and Naor [IPL'92] proved that this guarantee is optimal among deterministic algorithms when $Δ= O(\log n)$, and among randomized algorithms when $Δ= O(\sqrt{\log n})$. While deterministic improvements seemed out of reach, they conjectured that for graphs with $Δ= ω(\log n)$, randomized algorithms can achieve $(1 + o(1))Δ$ edge coloring. This conjecture was recently resolved in the affirmative: a $(1 + o(1))Δ$-coloring is achievable online using randomization for all graphs with $Δ= ω(\log n)$ [BSVW STOC'24]. Our results go further, uncovering two findings not predicted by the original conjecture. First, we give a deterministic online algorithm achieving $(1 + o(1))Δ$-colorings for all $Δ= ω(\log n)$. Second, we give a randomized algorithm achieving $(1 + o(1))Δ$-colorings already when $Δ= ω(\sqrt{\log n})$. Our results establish sharp thresholds for when greedy can be surpassed, and near-optimal guarantees can be achieved - matching the impossibility results of [BNMN IPL'92], both deterministically and randomly.

cs.DS↗

arXiv2025

Nearly Tight Sample Complexity for Matroid Online Contention Resolution

Due to their numerous applications, in particular in Mechanism Design, Prophet Inequalities have experienced a surge of interest. They describe competitive ratios for basic stopping time problems where random variables get revealed sequentially. A key drawback in the classical setting is the assumption of full distributional knowledge of the involved random variables, which is often unrealistic. A natural way to address this is via sample-based approaches, where only a limited number of samples from the distribution of each random variable is available. Recently, Fu, Lu, Gavin Tang, Wu, Wu, and Zhang (2024) showed that sample-based Online Contention Resolution Schemes (OCRS) are a powerful tool to obtain sample-based Prophet Inequalities. They presented the first sample-based OCRS for matroid constraints, which is a heavily studied constraint family in this context, as it captures many interesting settings. This allowed them to get the first sample-based Matroid Prophet Inequality, using $O(\log^4 n)$ many samples (per random variable), where $n$ is the number of random variables, while obtaining a constant competitiveness of $\frac{1}{4}-\varepsilon$. We present a nearly optimal sample-based OCRS for matroid constraints, which uses only $O(\log ρ\cdot \log^2\logρ)$ many samples, almost matching a known lower bound of $Ω(\log ρ)$, where $ρ\leq n$ is the rank of the matroid. Through the above-mentioned connection to Prophet Inequalities, this yields a sample-based Matroid Prophet Inequality using only $O(\log n + \logρ\cdot \log^2\logρ)$ many samples, and matching the competitiveness of $\frac{1}{4}-\varepsilon$, which is the best known competitiveness for the considered almighty adversary setting even when the distributions are fully known.

cs.DS↗

arXiv2024

The Cost of Consistency: Submodular Maximization with Constant Recourse

In this work, we study online submodular maximization, and how the requirement of maintaining a stable solution impacts the approximation. In particular, we seek bounds on the best-possible approximation ratio that is attainable when the algorithm is allowed to make at most a constant number of updates per step. We show a tight information-theoretic bound of $\tfrac{2}{3}$ for general monotone submodular functions, and an improved (also tight) bound of $\tfrac{3}{4}$ for coverage functions. Since both these bounds are attained by non poly-time algorithms, we also give a poly-time randomized algorithm that achieves a $0.51$-approximation. Combined with an information-theoretic hardness of $\tfrac{1}{2}$ for deterministic algorithms from prior work, our work thus shows a separation between deterministic and randomized algorithms, both information theoretically and for poly-time algorithms.

cs.DS↗

arXiv2024

Data-Driven Solution Portfolios

In this paper, we consider a new problem of portfolio optimization using stochastic information. In a setting where there is some uncertainty, we ask how to best select $k$ potential solutions, with the goal of optimizing the value of the best solution. More formally, given a combinatorial problem $Π$, a set of value functions $V$ over the solutions of $Π$, and a distribution $D$ over $V$, our goal is to select $k$ solutions of $Π$ that maximize or minimize the expected value of the {\em best} of those solutions. For a simple example, consider the classic knapsack problem: given a universe of elements each with unit weight and a positive value, the task is to select $r$ elements maximizing the total value. Now suppose that each element's weight comes from a (known) distribution. How should we select $k$ different solutions so that one of them is likely to yield a high value? In this work, we tackle this basic problem, and generalize it to the setting where the underlying set system forms a matroid. On the technical side, it is clear that the candidate solutions we select must be diverse and anti-correlated; however, it is not clear how to do so efficiently. Our main result is a polynomial-time algorithm that constructs a portfolio within a constant factor of the optimal.

cs.DS↗

arXiv2024

Could ChatGPT get an Engineering Degree? Evaluating Higher Education Vulnerability to AI Assistants

AI assistants are being increasingly used by students enrolled in higher education institutions. While these tools provide opportunities for improved teaching and education, they also pose significant challenges for assessment and learning outcomes. We conceptualize these challenges through the lens of vulnerability, the potential for university assessments and learning outcomes to be impacted by student use of generative AI. We investigate the potential scale of this vulnerability by measuring the degree to which AI assistants can complete assessment questions in standard university-level STEM courses. Specifically, we compile a novel dataset of textual assessment questions from 50 courses at EPFL and evaluate whether two AI assistants, GPT-3.5 and GPT-4 can adequately answer these questions. We use eight prompting strategies to produce responses and find that GPT-4 answers an average of 65.8% of questions correctly, and can even produce the correct answer across at least one prompting strategy for 85.1% of questions. When grouping courses in our dataset by degree program, these systems already pass non-project assessments of large numbers of core courses in various degree programs, posing risks to higher education accreditation that will be amplified as these models improve. Our results call for revising program-level assessment design in higher education in light of advances in generative AI.

cs.CY↗

arXiv2024

Deterministic Online Bipartite Edge Coloring

We study online bipartite edge coloring, with nodes on one side of the graph revealed sequentially. The trivial greedy algorithm is $(2-o(1))$-competitive, which is optimal for graphs of low maximum degree, $Δ=O(\log n)$ [BNMN IPL'92]. Numerous online edge-coloring algorithms outperforming the greedy algorithm in various settings were designed over the years (e.g., AGKM FOCS'03, BMM SODA'10, CPW FOCS'19, BGW SODA'21, KLSST STOC'22, BSVW STOC'24), all crucially relying on randomization. A commonly-held belief, first stated by [BNMN IPL'92], is that randomization is necessary to outperform greedy. Surprisingly, we refute this belief, by presenting a deterministic algorithm that beats greedy for sufficiently large $Δ=Ω(\log n)$, and in particular has competitive ratio $\frac{e}{e-1}+o(1)$ for all $Δ=ω(\log n)$. We obtain our result via a new and surprisingly simple randomized algorithm that works against adaptive adversaries (as opposed to oblivious adversaries assumed by prior work), which implies the existence of a similarly-competitive deterministic algorithm [BDBKTW STOC'90].

cs.DS↗

arXiv2024

Asymptotically Optimal Hardness for $k$-Set Packing and $k$-Matroid Intersection

For any $\varepsilon > 0$, we prove that $k$-Dimensional Matching is hard to approximate within a factor of $k/(12 + \varepsilon)$ for large $k$ unless $\textsf{NP} \subseteq \textsf{BPP}$. Listed in Karp's 21 $\textsf{NP}$-complete problems, $k$-Dimensional Matching is a benchmark computational complexity problem which we find as a special case of many constrained optimization problems over independence systems including: $k$-Set Packing, $k$-Matroid Intersection, and Matroid $k$-Parity. For all the aforementioned problems, the best known lower bound was a $Ω(k /\log(k))$-hardness by Hazan, Safra, and Schwartz. In contrast, state-of-the-art algorithms achieved an approximation of $O(k)$. Our result narrows down this gap to a constant and thus provides a rationale for the observed algorithmic difficulties. The crux of our result hinges on a novel approximation preserving gadget from $R$-degree bounded $k$-CSPs over alphabet size $R$ to $kR$-Dimensional Matching. Along the way, we prove that $R$-degree bounded $k$-CSPs over alphabet size $R$ are hard to approximate within a factor $Ω_k(R)$ using known randomised sparsification methods for CSPs.

cs.CC↗

arXiv2024

Online Edge Coloring is (Nearly) as Easy as Offline

The classic theorem of Vizing (Diskret. Analiz.'64) asserts that any graph of maximum degree $Δ$ can be edge colored (offline) using no more than $Δ+1$ colors (with $Δ$ being a trivial lower bound). In the online setting, Bar-Noy, Motwani and Naor (IPL'92) conjectured that a $(1+o(1))Δ$-edge-coloring can be computed online in $n$-vertex graphs of maximum degree $Δ=ω(\log n)$. Numerous algorithms made progress on this question, using a higher number of colors or assuming restricted arrival models, such as random-order edge arrivals or vertex arrivals (e.g., AGKM FOCS'03, BMM SODA'10, CPW FOCS'19, BGW SODA'21, KLSST STOC'22). In this work, we resolve this longstanding conjecture in the affirmative in the most general setting of adversarial edge arrivals. We further generalize this result to obtain online counterparts of the list edge coloring result of Kahn (J. Comb. Theory. A'96) and of the recent "local" edge coloring result of Christiansen (STOC'23).

cs.DS↗

arXiv2023

Simple and Asymptotically Optimal Online Bipartite Edge Coloring

We provide a simple online $Δ(1+o(1))$-edge-coloring algorithm for bipartite graphs of maximum degree $Δ=ω(\log n)$ under adversarial vertex arrivals on one side of the graph. Our algorithm slightly improves the result of (Cohen, Peng and Wajc, FOCS19), which was the first, and currently only, to obtain an asymptotically optimal $Δ(1+o(1))$ guarantee for an adversarial arrival model. More importantly, our algorithm provides a new, simpler approach for tackling online edge coloring.

cs.DS↗