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Algorithmic algorithm development with LLMs: A Case Study on LLM-Usage for Contraction Order Optimization in Tensor Networks
arXiv:2606.01975v1 Announce Type: new Abstract: We consider LLM-based algorithm development through a case study on contractionorder optimisation for tensor networks with OpenEvolve. We pay particular attention to the choice of the LLM as well as design choices such as evaluation metric and test instances. Our results highlight both the promise of verifier-guided evolutionary coding agents for algorithm development/improvement and the continuing importance of evaluation, validation, and...
Mean-based algorithms: A lower bound and regret
Announce Type: new Abstract: Mean-based algorithms are a class of online learning algorithms that assign low probability to actions with low average rewards. Recent work indicates these algorithms converge favorably to serially undominated actions, which approximate Nash equilibria in economic games. However, empirical studies also show slower convergence compared to established algorithms in bandit-feedback scenarios.
An Efficient Genus Algorithm Based on Graph Rotations
arXiv:2411.07347v5 Announce Type: replace Abstract: We study the problem of determining the minimal genus of a simple finite connected graph. We present an algorithm which, for an arbitrary graph $G$ with $n$ vertices and $m$ edges, determines the orientable genus of $G$ in $O(n(4^m/n)^{n/t})$ steps where $t$ is the girth of $G$. This algorithm avoids difficulties that many other genus algorithms have with handling bridge placements which is a well-known issue. The algorithm has a number of...
Algorithmic Monocultures in Hiring
Over 90% of U.S. employers rely on hiring algorithms to screen job applicants. Many different employers use algorithms from the same few vendors. We conduct the largest empirical study of algorithmic hiring with data for 3.4 million real job applicants submitting 4 million applications to 156 employers across 11 market sectors.
Efficient Parallel Algorithms for Hypergraph Matching
arXiv:2602.22976v3 Announce Type: replace Abstract: We present efficient parallel algorithms for computing maximal matchings in hypergraphs. Our algorithm finds locally maximal edges in the hypergraph and adds them in parallel to the matching. In the CRCW PRAM models our algorithms achieve $O(\log{\log{\Delta}}\log{m})$ time with $O(\kappa\log {m})$ work w.h.p. where $m$ is the number of hyperedges, and $\kappa$ is the sum and $\Delta$ is the maximum of all vertex degrees.
Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms
Announce Type: replace Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems. In this paper, we consider the problem of improving the average-case performance of an algorithm over a specific distribution of problem instances. While this task can be tackled by embedding trainable components into the algorithm updates, a key challenge is to preserve worst-case guarantees across the entire...
Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Models
arXiv:2508.11874v2 Announce Type: replace Abstract: Designing polynomial-time algorithms for approximate Nash equilibria (ANE) with provable worst-case guarantees is a fundamental open problem in algorithmic game theory. While large language models (LLMs) can generate candidate algorithms at scale, certifying worst-case guarantees requires formal analysis over all game instances -- a task for which no automated system previously existed. Here, we present LegoNE, a framework encoding expert...
On the History of the Square and Multiply Algorithm
arXiv:2606.00958v2 Announce Type: replace-cross Abstract: The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a technique for fast exponentiation commonly used in modern cryptography and computational number theory. Despite its prominence, the historical origins of the algorithm are not known with certainty. This paper critically examines the origins and formalization of the algorithm through primary source analysis.
On the History of the Square and Multiply Algorithm
arXiv:2606.00958v1 Announce Type: cross Abstract: The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a technique for fast exponentiation commonly used in modern cryptography and computational number theory. Despite its prominence, the historical origins of the algorithm are not known with certainty. This paper critically examines the origins and formalization of the algorithm through primary source analysis.
You can personalize your Instagram algorithm now — unless you want to see more posts from accounts you follow
You can personalize your Instagram algorithm now — unless you want to see more posts from accounts you follow The app expanded its algorithm personalization features to its main feed. Instagram just made it a whole lot easier to control what you see in your main feed. The app expanded its algorithm personalization feature to its central feed so users can choose exactly what topics they want to see more and less of in their recommendations.