Related papers: Polynomial-time algorithms for the curve graph
In this paper an algorithm is given to determine all possible structurally different linearly conjugate realizations of a given kinetic polynomial system. The solution is based on the iterative search for constrained dense realizations…
We estimate the distance in the curve graph of a surface S of finite type using Teichmueller geodesics and assuming to be able to detect curves of distance at least three.
We show that there exists a polynomial algorithm to pack interval graphs with vertex-disjoint triangles.
We study the problem of computing the diameter and the mean distance of a continuous graph, i.e., a connected graph where all points along the edges, instead of only the vertices, must be taken into account. It is known that for continuous…
Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…
We present a certified algorithm that takes a smooth algebraic curve in $\mathbb{R}^n$ and computes an isotopic approximation for a generic projection of the curve into $\mathbb{R}^2$. Our algorithm is designed for curves given implicitly…
We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges. Using symplectic geometry, sampling such polygons reduces to sampling a moment…
We present an algorithm for the computation of period matrices and the Abel-Jacobi map of complex superelliptic curves given by an equation $y^m=f(x)$. It relies on rigorous numerical integration of differentials between Weierstrass points,…
A graph separator is a subset of vertices of a graph whose removal divides the graph into small components. Computing small graph separators for various classes of graphs is an important computational task. In this paper, we present a…
The outcomes of this paper are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class PTIME of languages computable in…
The median of a set of vertices $P$ of a graph $G$ is the set of all vertices $x$ of $G$ minimizing the sum of distances from $x$ to all vertices of $P$. In this paper, we present a linear time algorithm to compute medians in median graphs,…
In this paper, we give a polynomial-time algorithm for deciding whether an input bipartite graph admits a 2-layer fan-planar drawing, resolving an open problem posed in several papers since 2015.
The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We present an efficient…
We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on $n$ vertices. Our algorithm solves a more general problem: given $n$ and $\omega$ as input, it computes the number of…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…
We give the first polynomial-time algorithm for coloring vertices of P_5-free graphs with k colors. This settles an open problem and generalizes several previously known results.
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…