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Vsevolod Chernyshev

Publications and source records attributed to Vsevolod Chernyshev.

7 recordsLinked to original sources
arXiv2026

Upper Bound for Permanent Saturation of Metric Graphs using Interval Exchange Transformations

We study upper bounds for the moment of permanent $\varepsilon$-saturation in finite metric graphs. The dynamics is generated by moving points travelling with unit speed along edges and branching into all outgoing directions whenever they reach a vertex. We first reformulate this branched dynamics in terms of birth times at vertices and prove a sufficient same-time criterion for permanent $\varepsilon$-saturation. The main rigorous estimate is obtained from a rotation, regarded as a two-interval exchange transformation. More precisely, if the graph contains two closed walks based at the initial vertex whose lengths have irrational ratio, then the covering properties of the corresponding rotation imply an explicit upper bound for the permanent saturation time. In particular, bounded-type rotations yield a bound of order $\varepsilon^{-1}$. We also construct a more general auxiliary interval exchange transformation on the set of oriented edges. This construction depends on cyclic orders at the vertices and organizes the ordered edge-state data of the graph. Since the branched graph dynamics is non-invertible, whereas an interval exchange transformation is invertible away from discontinuities, this auxiliary IET is not identified with the full graph dynamics. Instead, we formulate the additional birth-time transfer property required for recurrence estimates of the auxiliary IET to imply saturation bounds. We also discuss rotation-type and non-rotation examples of graph-induced self-similar IETs, together with numerical illustrations for star and complete graphs.

math.DS↗
arXiv2026

DFS-based fast crack pre-detection

This paper develops a computationally efficient pre-detection method for cracks in three-dimensional CT images of concrete. Instead of attempting full voxel-wise crack segmentation, the method focuses on locating cubic subregions where crack structures are likely to be present and should be analyzed further. The proposed pipeline combines multiscale Maximal Hessian Entry filtering with graph-based connectivity analysis. After binarization, each subregion is represented by the boundary face with the largest foreground pixels, which transforms the local detection problem from a three-dimensional image task into a two-dimensional graph problem. A sparse lattice graph is constructed on the selected face, and Depth-First Search is applied to detect connected components corresponding to possible crack cross-sections. The choice of mesh size is justified by a probabilistic upper bound on a lattice-miss event. Experiments on semi-synthetic and real CT data show that the method gives fast, interpretable crack pre-localization while avoiding exhaustive analysis of the full image.

eess.IV↗
arXiv2025

A Faster Algorithm for Independent Cut

The previously fastest algorithm for deciding the existence of an independent cut had a runtime of $\mathcal{O}^*(1.4423^n)$, where $n$ is the order of the input graph. We improve this to $\mathcal{O}^*(1.4143^n)$. In fact, we prove a runtime of $\mathcal{O}^*\left( 2^{(\frac{1}{2}-α_Δ)n} \right)$ on graphs of order $n$ and maximum degree at most $Δ$, where $α_Δ=\frac{1}{2+4\lfloor \fracΔ{2} \rfloor}$. Furthermore, we show that the problem is fixed-parameter tractable on graphs of order $n$ and minimum degree at least $βn$ for some $β> \frac{1}{2}$, where $β$ is the parameter.

cs.DS↗
arXiv2025

The Canadian Traveller Problem on outerplanar graphs

We study the $k$-Canadian Traveller Problem, where a weighted graph $G=(V,E,ω)$ with a source $s\in V$ and a target $t\in V$ are given. This problem also has a hidden input $E_* \subsetneq E$ of cardinality at most $k$ representing blocked edges. The objective is to travel from $s$ to $t$ with the minimum distance. At the beginning of the walk, the blockages $E_*$ are unknown: the traveller discovers that an edge is blocked when visiting one of its endpoints. Online algorithms, also called strategies, have been proposed for this problem and assessed with the competitive ratio, {\em i.e.}, the ratio between the distance actually traversed by the traveller divided by the distance he would have traversed knowing the blockages in advance. Even though the optimal competitive ratio is $2k+1$ even on unit-weighted planar graphs of treewidth 2, we design a polynomial-time strategy achieving competitive ratio 9 on unit-weighted outerplanar graphs. This value 9 also stands as a lower bound for this family of graphs as we prove that, for any $\varepsilon > 0$, no strategy can achieve a competitive ratio $9-\varepsilon$ on it. This comes actually from a strong connexion with another well-known online problem called the cow-path problem. Finally, we show that it is not possible to achieve a competitive ratio $e^{W(\frac{\ln k}{2})} - 1$ on arbitrarily weighted outerplanar graphs, where $W$ is the Lambert W function. This lower bound is asymptotically greater than $\frac{\ln k}{\ln \ln k}$.

cs.DS↗
arXiv2024

Forest Cuts in Sparse Graphs

We propose the conjecture that every graph $G$ of order $n$ with less than $3n-6$ edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts and show that the density condition would be best possible. We verify the conjecture for planar graphs and show that every graph $G$ of order $n$ with less than $\frac{11}{5}n-\frac{18}{5}$ edges has a vertex cut that induces a forest.

math.CO↗