Related papers: Robust certified numerical homotopy tracking
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise).…
Given an undirected graph, $G$, and vertices, $s$ and $t$ in $G$, the tracking paths problem is that of finding the smallest subset of vertices in $G$ whose intersection with any $s$-$t$ path results in a unique sequence. This problem is…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…
In this paper, motivated by the setting of white-space detection [1], we present theoretical and empirical results for detection of the zero-support E of x \in Cp (xi = 0 for i \in E) with reduced-dimension linear measurements. We propose…
In this paper, we transfer the problem of measuring navigational complexity in topological spaces to the nearness theory. We investigate the most important component of this problem, the topological complexity number (denoted by TC), with…
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…
In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
We consider first the zero-nonzero determination problem, which consists in determining the list of zero-nonzero conditions realized by a finite list of polynomials on a finite set Z included in C^k with C an algebraic closed field. We…
We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(n D kappa(f)) iterations where n is the number of polynomials (as well as the dimension of the ambient space), D…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
Zero-free based algorithm is a major technique for deterministic approximate counting. In Barvinok's original framework[Bar17], by calculating truncated Taylor expansions, a quasi-polynomial time algorithm was given for estimating zero-free…
A polynomial time algorithm which detects all paths and cycles of all lengths in form of vertex pairs (start, finish).
In this paper a search algorithm is proposed to find a sub optimal path for a non-holonomic system. For this purpose the algorithm starts sampling the front part of the vehicle and moves towards the destination with a cost function. The…