Hubert Chathi

• Master of Math
• Developer at New Vector Ltd

Upward planarity testing, or checking whether a directed graph has a drawing in which no edges cross and all edges point upward, is NP-complete. All of the algorithms for upward planarity testing developed previously focused on special classes of graphs. In this paper we develop a parameterized algorithm for upward planarity testing that can be app...

Abstract We can visualize a graph,by producing,a geometric,representation,of the graph,in which each node is represented by a single point on the plane, and each edge is represented by a curve that connects,its two endpoints. Directed graphs,are often used to model,hierarchical,structures; in order to visualize the hierarchy represented by such a g...

Filtering is a method of estimating the conditional probability distribution of a signal based upon a noisy, partial, corrupted sequence of observations of the signal. Particle filters are a method of filtering in which the conditional distribution of the signal state is approximated by the empirical measure of a large collection of particles, each...

A branching particle-based filter is used to detect and track multiple simulated maneuvering ships in a region of water. The ship trajectories exhibit nonlinear dynamics and interact in a nonlinear manner so that the ships do not collide. There is no a priori knowledge of the number of ships in the region. Observations model a sensor tracking the s...

Particle approximations are used to track a maneuvering signal given only a noisy, corrupted sequence of observations, as are encountered in target tracking and surveillance. The signal exhibits nonlinearities that preclude the optimal use of a Kalman filter. It obeys a stochastic differential equation (SDE) in a seven-dimensional state space, one...