Tootfinder

Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric
Iman Seyedi, Antonio Candelieri, Enza Messina, Francesco Archetti
https://arxiv.org/abs/2509.04089

Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric
The assignment problem, a cornerstone of operations research, seeks an optimal one-to-one mapping between agents and tasks to minimize total cost. This work traces its evolution from classical formulations and algorithms to modern optimal transport (OT) theory, positioning the Quadratic Assignment Problem (QAP) and related structural matching tasks within this framework. We connect the linear assignment problem to Monge's transport problem, Kantorovich's relaxation, and Wasserstein distances, t…

The Log-Rank Conjecture: New Equivalent Formulations
Lianna Hambardzumyan, Shachar Lovett, Morgan Shirley
https://arxiv.org/abs/2510.02583 https://arxiv.or…

The Log-Rank Conjecture: New Equivalent Formulations
The log-rank conjecture is a longstanding open problem with multiple equivalent formulations in complexity theory and mathematics. In its linear-algebraic form, it asserts that the rank and partitioning number of a Boolean matrix are quasi-polynomially related. We propose a relaxed but still equivalent version of the conjecture based on a new matrix parameter, signed rectangle rank: the minimum number of all-1 rectangles needed to express the Boolean matrix as a $\pm 1$-sum. Signed rectangle …

A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
Francisco Daunas, I\~naki Esnaola, Samir M. Perlaza
https://arxiv.org/abs/2508.03314 htt…

A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
The dual formulation of empirical risk minimization with f-divergence regularization (ERM-fDR) is introduced. The solution of the dual optimization problem to the ERM-fDR is connected to the notion of normalization function introduced as an implicit function. This dual approach leverages the Legendre-Fenchel transform and the implicit function theorem to provide a nonlinear ODE expression to the normalization function. Furthermore, the nonlinear ODE expression and its properties provide a compu…

EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design
Fei Liu, Yilu Liu, Qingfu Zhang, Xialiang Tong, Mingxuan Yuan
https://arxiv.org/abs/2508.03082 https:…

EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design
Automated Heuristic Design (AHD) using Large Language Models (LLMs) has achieved notable success in recent years. Despite the effectiveness of existing approaches, they only design a single heuristic to serve all problem instances, often inducing poor generalization across different distributions or settings. To address this issue, we propose Automated Heuristic Set Design (AHSD), a new formulation for LLM-driven AHD. The aim of AHSD is to automatically generate a small-sized complementary heur…

Constraint Satisfaction Approaches to Wordle: Novel Heuristics and Cross-Lexicon Validation
Jahidul Arafat, Fariha Tasmin, Sanjaya Poudel, Kamrujjaman, Eftakhar Ahmed Arnob, Ahsan Habib Tareq
https://arxiv.org/abs/2510.02855

Constraint Satisfaction Approaches to Wordle: Novel Heuristics and Cross-Lexicon Validation
Wordle presents an algorithmically rich testbed for constraint satisfaction problem (CSP) solving. While existing solvers rely on information-theoretic entropy maximization or frequency-based heuristics without formal constraint treatment, we present the first comprehensive CSP formulation of Wordle with novel constraint-aware solving strategies. We introduce CSP-Aware Entropy, computing information gain after constraint propagation rather than on raw candidate sets, and a Probabilistic CSP fra…

ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions
Wei Cai, Andrew Qing He
https://arxiv.org/abs/2509.03757

ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions
We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference operator onto the test function. The main advantage of this framework is that it is fully derivative-free with respect to the solution neural network. This framework is particularly suitable for Fokker-Planck type second-order elliptic and parabolic PDEs.

Action principle for $\kappa$-Minkowski noncommutative $U(1)$ gauge theory from Lie-Poisson electrodynamics
Maxim Kurkov
https://arxiv.org/abs/2509.03714 https://

Action principle for $κ$-Minkowski noncommutative $U(1)$ gauge theory from Lie-Poisson electrodynamics
Lie-Poisson electrodynamics describes a semi-classical approximation of noncommutative $U(1)$ gauge theories with Lie-algebra-type noncommutativities. We obtain a gauge-invariant local classical action with the correct commutative limit for a generic Lie-Poisson gauge model. At the semi-classical level, our results provide a relatively simple solution to the old problem of constructing an admissible Lagrangian formulation for the $U(1)$ gauge theory on the four-dimensional $κ$-Minkowski space-…

Some Remarks on the $l_1$-Robust Solution of LexRank Problem
Anna Timonina-Farkas
https://arxiv.org/abs/2509.04131 https://arxiv.org/pdf/2509.04131

Some Remarks on the $l_1$-Robust Solution of LexRank Problem
Graph-based ranking methods, such as LexRank, are fundamental in Natural Language Processing (NLP) applications like text summarization, as they measure the relative importance of textual units. Building on recent advances in ranking methods for growing and dynamic graphs, we develop a robust variant of LexRank that operates on stochastic similarity graphs with uncertain and expanding structure. Our approach introduces a novel $l_1$-based formulation that captures ambiguity in both transition p…

On computing sparse universal solvers for key problems in statistics
Ananias Sousa Machado, Marcia Fampa, Jon Lee
https://arxiv.org/abs/2509.04264 https://…

On computing sparse universal solvers for key problems in statistics
We give sparsity results and present algorithms for calculating minimum (vector) 1-norm universal solvers connected to least-squares problems. In particular, besides universal least-squares solvers, we consider minimum-rank universal least-squares solvers, and simultaneous universal minimum-norm/least-squares solvers. For all of these, we present and compare several new alternative linear-optimization formulations and very effective proximal-point algorithms. Overall, we found that our new Doug…

Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques
Zhong Zhang, Xiang Guo, Di Wu, Hexi Baoyin, Junfeng Li, Francesco Topputo
https://arxiv.org/abs/2508.02904

Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques
Designing optimal trajectories for multi-flyby asteroid missions is scientifically critical but technically challenging due to nonlinear dynamics, intermediate constraints, and numerous local optima. This paper establishes a method that approaches global optimality for multi-flyby trajectory optimization under a given sequence. The original optimal control problem with interior-point equality constraints is transformed into a multi-stage decision formulation. This reformulation enables direct a…