arXiv subjects

Dávid Ferenczi

Publications and source records attributed to Dávid Ferenczi.

3 recordsLinked to original sources

arXiv2026

Local Search for Almost-Spanning Square Grids in Erdős--Rényi Random Graphs

Finding large lattice subgraphs in sparse Erdős--Rényi random graphs is a classical problem at the interface of random graph theory and algorithms. General bounded-degree embedding and universality theorems give powerful results for broad graph families, but when specialized to square grids they operate at densities substantially larger than the grid-emergence scale. In this paper we exploit the specific geometry of the square grid. We introduce the Quarantined Local Search, a three-phase local algorithm that separates the construction of an initial boundary from the later corner-closure process and controls adaptive negative exposure through bounded pair-test histories. We prove that, for every fixed $δ\in (0,1)$, there exists $C_δ>0$ such that the algorithm embeds a $k\times k$ square grid with $k^2\le (1-δ)n$ in $G(n,p)$ with high probability whenever $p\ge C_δ\sqrt{\ln k/n}$. Thus, for $k^2=Θ(n)$, a density of order $\sqrt{\log n/n}$ is sufficient, a factor of order $\sqrt{\log n}$ above the corresponding $n^{-1/2}$ emergence scale.

math.PR↗

arXiv2026

Inferring signed social networks from contact patterns

Social networks are typically inferred from indirect observations, such as proximity data; yet, most methods cannot distinguish between absent relationships and actual negative ties, as both can result in few or no interactions. We address the challenge of inferring signed networks from contact patterns while accounting for whether lack of interactions reflect a lack of opportunity as opposed to active avoidance. We develop a Bayesian framework with MCMC inference that models interaction groups to separate chance from choice when no interactions are observed. Validation on synthetic data demonstrates superior performance compared to natural baselines, particularly in detecting negative edges. We apply our method to French high school contact data to reveal a structure consistent with friendship surveys and demonstrate the model's adequacy through posterior predictive checks.

cs.SI↗

arXiv2026

Constrained graph generation: Preserving diameter and clustering coefficient simultaneously

Generating graphs subject to strict structural constraints is a fundamental computational challenge in network science. Simultaneously preserving interacting properties-such as the diameter and the clustering coefficient- is particularly demanding. Simple constructive algorithms often fail to locate vanishingly small sets of feasible graphs, while traditional Markov-chain Monte Carlo (MCMC) samplers suffer from severe ergodicity breaking. In this paper, we propose a two-step hybrid framework combining Ant Colony Optimization (ACO) and MCMC sampling. First, we design a layered ACO heuristic to perform a guided global search, effectively locating valid graphs with prescribed diameter and clustering coefficient. Second, we use these ACO-designed graphs as structurally distinct seed states for an MCMC rewiring algorithm. We evaluate this framework across a wide range of graph edge densities and varying diameter-clustering-coefficient constraint regimes. Using the spectral distance of the normalized Laplacian to quantify structural diversity of the resulting graphs, our experiments reveal a sharp contrast between the methods. Standard MCMC samplers remain rigidly trapped in an isolated subset of feasible graphs around their initial seeds. Conversely, our hybrid ACO-MCMC approach successfully bridges disconnected configuration landscapes, generating a vastly richer and structurally diverse set of valid graphs.

cs.SI↗