Approximation algorithms for spreading points

Approximation Algorithms for Spreading Points

We consider the problem of placing n points, each one inside its own, prespecified disk, with the objective of maximizing the distance between the closest pair of them. The disks can overlap and have different sizes. The problem is NP-hard and does not admit a PTAS. In the L∞ metric, we give a 2-approximation algorithm running in O(n √ n log n) time. In the L2 metric, we give a quadratic time a...

Stability and instability of limit points for stochastic approximation algorithms

It is shown that the limit points of a stochastic approximation (SA) algorithm compose a connected set. Conditions are given to guarantee the uniqueness of the limit point for a given initial value. Examples are provided wherein of SA algorithm converges to a limit independent of initial values, but is unstable for the differential equation _ = ( ) with a nonnegative Lyapunov function. Finally,...

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)