Zobrazeno 1 - 10
of 93
pro vyhledávání: '"de Mesmay, Arnaud"'
While the problem of computing the genus of a knot is now fairly well understood, no algorithm is known for its four-dimensional variants, both in the smooth and in the topological locally flat category. In this article, we investigate a class of kno
Externí odkaz:
http://arxiv.org/abs/2312.09094
Autor:
Cohen-Addad, Vincent, Fan, Chenglin, Ghoshal, Suprovat, Lee, Euiwoong, de Mesmay, Arnaud, Newman, Alantha, Wang, Tony Chang
We consider the Low Rank Approximation problem, where the input consists of a matrix $A \in \mathbb{R}^{n_R \times n_C}$ and an integer $k$, and the goal is to find a matrix $B$ of rank at most $k$ that minimizes $\| A - B \|_0$, which is the number
Externí odkaz:
http://arxiv.org/abs/2311.00892
The degenerate crossing number of a graph is the minimum number of transverse crossings among all its drawings, where edges are represented as simple arcs and multiple edges passing through the same point are counted as a single crossing. Interpretin
Externí odkaz:
http://arxiv.org/abs/2308.10666
Autor:
Lunel, Corentin, de Mesmay, Arnaud
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants and properti
Externí odkaz:
http://arxiv.org/abs/2303.07982
The main goal of this paper is to investigate the minimal size of families of curves on surfaces with the following property: a family of simple closed curves $\Gamma$ on a surface realizes all types of pants decompositions if for any pants decomposi
Externí odkaz:
http://arxiv.org/abs/2302.06336
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 26:2, Discrete Algorithms (August 20, 2024) dmtcs:10810
A matroid $M$ is an ordered pair $(E,I)$, where $E$ is a finite set called the ground set and a collection $I\subset 2^{E}$ called the independent sets which satisfy the conditions: (i) $\emptyset \in I$, (ii) $I'\subset I \in I$ implies $I'\in I$, a
Externí odkaz:
http://arxiv.org/abs/2301.03221
Given $x \in (\mathbb{R}_{\geq 0})^{\binom{[n]}{2}}$ recording pairwise distances, the METRIC VIOLATION DISTANCE (MVD) problem asks to compute the $\ell_0$ distance between $x$ and the metric cone; i.e., modify the minimum number of entries of $x$ to
Externí odkaz:
http://arxiv.org/abs/2208.13920
In this article, we investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result is a polynomial-time algorithm that for any graph embedded in a non-orientable surface computes a cano
Externí odkaz:
http://arxiv.org/abs/2203.06659
Autor:
Chartier, Jean, de Mesmay, Arnaud
A closed quasigeodesic on a convex polyhedron is a closed curve that is locally straight outside of the vertices, where it forms an angle at most $\pi$ on both sides. While the existence of a simple closed quasigeodesic on a convex polyhedron has bee
Externí odkaz:
http://arxiv.org/abs/2203.05853
An approximation algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying a $(1 - f(\epsilon))$-fraction of the constraints on any $(1-\epsilon)$-satisfiable instance, where the loss function $f$ is such
Externí odkaz:
http://arxiv.org/abs/2110.11851