Related papers: Certified algebraic curve projections by path trac…
In the present paper, we study algorithmic questions for the arc-intersection graph of directed paths on a tree. Such graphs are known to be perfect (proved by Monma and Wei in 1986). We present faster algorithms than all previously known…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may have up to eight nodes, or a triple point of a given type and…
We study the problem of planning paths for a team of robots for visually monitoring an environment. Our work is motivated by surveillance and persistent monitoring applications. We are given a set of target points in a polygonal environment…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
We propose sublinear algorithms for probabilistic testing of the discrete and continuous Fr\'echet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guarantee the correctness of the monodromy action produced by the…
Maintaining the visibility of the target is one of the major objectives of aerial tracking missions. This paper proposes a target-visible trajectory planning pipeline using quadratic programming. Our approach can handle various tracking…
An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant…
Given a smooth complex variety $X$, an algebraically skew embedding of $X$ is an embedding of $X$ into a complex projective space $\mathbb{P}^N$ such that for any two points $x,y\in X$, their embedded tangent spaces in $\mathbb{P}^N$ do not…
An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…
In this article, we study isomorphisms between complements of irreducible curves in the projective plane $\mathbb{P}^2$, over an arbitrary algebraically closed field. Of particular interest are rational unicuspidal curves. We prove that if…
The problem of constructing elliptic curves suitable for pairing applications has received a lot of attention. To solve this, we propose a variant algorithm of a known method by Brezing and Weng. We produce new families of parameters using…
We present an algorithm for constructing a map $\mathbb{P}^2\to\mathbb{P}^2$ with a given branching curve. The stepping stone is the ramification curve, which is obtained as the linear normalization of the branching curve.
Path generation, the process of converting high-level mission specifications, such as sequences of waypoints from a path planner, into smooth, executable paths, is a fundamental challenge in mobile robotics. Most path following and…
Many applications of geometry modeling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In this paper, we define the notion of the discrete geodesic curvature of a geodesic polygon on a…