arXiv subjects

Henrique Assumpção

Publications and source records attributed to Henrique Assumpção.

3 recordsLinked to original sources

arXiv2026

CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization

We introduce CodeEvolve, an open-source framework that couples large language models with island-based evolutionary search for end-to-end algorithmic discovery. CodeEvolve integrates inspiration-based crossover, meta-prompting, and depth-based refinement on top of a CVT-MAP-Elites archive and a weighted LLM ensemble to generate optimized solutions for complex problems. On the AlphaEvolve benchmark suite, CodeEvolve matches or surpasses the reported AlphaEvolve results on 5 of 9 problems and, under matched conditions, outperforms the open-source frameworks OpenEvolve and ShinkaEvolve on 6 of 9. With the open-weight Qwen3-Coder-30B backbone, it surpasses the reported AlphaEvolve score on both CirclePackingSquare instances at roughly an order of magnitude lower cost than a frontier closed-source ensemble, and remains competitive with EoH on heuristic-design tasks without retuning. Ablations show that the interaction between CodeEvolve's components, rather than any single operator, drives these results. We release the framework, experimental data, and practical hyperparameter guidelines at https://github.com/inter-co/science-codeevolve.

cs.AI↗

arXiv2026

Total Conformal Rigidity in Graphs

We introduce and study a generalization of conformal rigidity for graphs. A graph is $k$-conformally rigid if the uniform edge weights simultaneously maximize the sum of the $k$ smallest nontrivial Laplacian eigenvalues and minimize the sum of the $k$ largest, over all normalized non-negative weight assignments. A graph that is $k$-conformally rigid for every $k$ is called totally conformally rigid. Our main result is a complete characterization: a graph is totally conformally rigid if and only if it is edge-rigid, meaning every canonical spectral embedding onto a Laplacian eigenspace is edge-isometric. We further show this is equivalent to all edges of the graph being pairwise Laplacian-cospectral, that is, the removal of any single edge yields a graph with the same Laplacian characteristic polynomial. Using semidefinite programming duality, we establish this equivalence and derive a polynomial-time algorithm for deciding edge-rigidity using only integer arithmetic. We provide a combinatorial characterization of edge-rigidity in terms of Laplacian walks and connect it to the walk-regularity of signed line graphs. We show that a graph is edge-rigid if and only if it is either $1$-walk-regular or $1$-walk-biregular, and we finally show an equivalence based on monotone gauges and gauge duality. As an application, we derive two non-trivial combinatorial consequences of total conformal rigidity, relating it to the number of spanning trees and the Kirchhoff index of the graph.

math.CO↗

arXiv2026

Semidefinite programming bounds on fractional cut-cover and maximum 2-SAT for highly regular graphs

We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue. We also extend the equality cases of a primal-dual inequality involving the Goemans-Williamson semidefinite program, which approximates MAXCUT, to graphs in certain coherent configurations. Moreover, we obtain spectral bounds for MAX 2-SAT when the underlying graphs belong to a symmetric association scheme by means of a certain semidefinite program used to approximate quadratic programs, and we further develop this technique in order to explicitly compute the optimum value of its gauge dual in the case of distance-regular graphs.

math.OC↗