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Unless the targeted mesh is developable, metric distortion is inevitable during the process of surface mesh parameterization, thus one important objective of all involved parametric studies is to reduce the metric distortion. In order to further reduce area and angle distortion, a novel method of boundary-free mesh parameterization is presented in the paper. Firstly, the initial boundary-fixed conformal parameterization from 3D surface mesh patch to a plane is performed in the method. Then, based on the initial parameterization, the iterations of boundary-free quasi-harmonic parameterization are developed, where the tensor field is updated in each iterative step and the principal curvature direction is utilized to terminate the iteration. The solution of the novel method is convenient to calculate since it involves a series of linear systems. In our novel parameterization method, lower metric distortion and considerable efficiency have been obtained in experiments. [ABSTRACT FROM AUTHOR]

Inspired by current challenges in data-intensive and energy-limited sensor networks, we formulate a coverage optimization problem for mobile sensors as a (constrained) repeated multi-player game. Each sensor tries to optimize its own coverage while minimizing the processing/energy cost. The sensors are subject to the informational restriction that the environmental distribution function is unknown a priori. We present two distributed learning algorithms where each sensor only remembers its own utility values and actions played during the last plays. These algorithms are proven to be convergent in probability to the set of (constrained) Nash equilibria and global optima of a certain coverage performance metric, respectively. Numerical examples are provided to verify the performance of our proposed algorithms. [ABSTRACT FROM AUTHOR]

Abstract: A geometric spanning tree of a point set is a tree whose vertex set is and whose edge set is a set of non-crossing straight line segments with endpoints in . Given a set of red points and a set of blue points in the plane, the red/blue spanning tree problem is to find a geometric spanning tree for red points and a geometric spanning tree for blue points such that the number of crossing points of the two trees is a minimum. If no three points are collinear, we show that the minimum number of crossing points is completely determined by the number of maximal red (or blue) chains on the convex hull of all red points and blue points. We design an optimal algorithm for constructing a geometric spanning tree of all the red points and a geometric spanning tree of all the blue points with the minimum number of crossing points. If collinear points are allowed, we prove that the problem of deciding whether there exists a geometric spanning path of all the red points and a geometric spanning path of all the blue points without crossing is NP-complete. [Copyright &y& Elsevier]

In this paper we present an algorithm for the application of simultaneous localization and mapping in complex environments. Instead of building a grid map or building a feature map with a small number of the obstacles' geometric parameters, the proposed algorithm builds a sampled environment map (SEM) to represent a complex environment with a set of environment samples. To overcome the lack of one-toone correspondence between environment samples and raw observations, the signed orthogonal distance function is proposed to be used as the observation model. A method considering geometric constraints is presented to remove redundant environment samples from the SEM. We also present a method to improve the SEM's topological consistency by using corner constraints. The proposed algorithm has been verified in a simulation and an indoor experiment. The results show that the algorithm can localize the robot and build a complex map effectively. [ABSTRACT FROM AUTHOR]

Abstract: Given a set S of n points in , we wish to decide whether S has a subset of size at least k with Euclidean diameter at most r. It is unknown whether this decision problem is NP-hard. The two closely related optimization problems, (i) finding a largest subset of diameter at most r, and (ii) finding a subset of the smallest diameter of size at least k, were recently considered by Afshani and Chan. For maximizing the size, they presented several polynomial-time algorithms with constant approximation factors, the best of which has a factor of . For maximizing the diameter, they presented a polynomial-time approximation scheme. In this paper, we present improved approximation algorithms for both optimization problems. For maximizing the size, we present two algorithms: the first one improves the approximation factor to and the running time by an factor; the second one improves the approximation factor to 2 and the running time by an factor. For minimizing the diameter, we improve the running time of the PTAS from to . [Copyright &y& Elsevier]