Approximation Algorithms for Spreading Points

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+...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

22 Spreading Metrics For Vertex Ordering Problems ( Extended

We design approximation algorithms for the vertex ordering problems MINIMUM LINEAR ARRANGEMENT, MINIMUM CONTAINING INTERVAL GRAPH, and MINIMUM STORAGE-TIME PRODUCT, achieving approximation factors of O( √ log n log logn), O( √ logn log logn), and O( √ logT log logT ), respectively, the last running in time polynomial in T (T being the sum of execution times). The technical contribution of our p...

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

Approximate Hierarchical Clustering via Sparsest Cut and Spreading Metrics

Dasgupta recently introduced a cost function for the hierarchical clustering of a set of points given pairwise similarities between them. He showed that this function is NP -hard to optimize, but a top-down recursive partitioning heuristic based on an αn-approximation algorithm for uniform sparsest cut gives an approximation of O(αn logn) (the current best algorithm has αn = O( √ log n)). We sh...