Approximation Algorithms for Geometric Median Problems

Linear-Time Approximation Schemes for Clustering Problems

We present a general approach for designing approximation algorithms for a fundamental class of geometric clustering problems in arbitrary dimensions. More specifically, our approach leads to simple randomized algorithms for the k-means, k-median and discrete k-means problems that yield (1 + ε) approximations with probability ≥ 1/2 and running times of O(2(k/ε)O(1)dn). These are the first algor...

PERFORMANCE COMPARISON OF CBO AND ECBO FOR LOCATION FINDING PROBLEMS

The p-median problem is one of the discrete optimization problem in location theory which aims to satisfy total demand with minimum cost. A high-level algorithmic approach can be specialized to solve optimization problem. In recent years, meta-heuristic methods have been applied to support the solution of Combinatorial Optimization Problems (COP). Collision Bodies Optimization algorithm (CBO) a...

Effectiveness of Local Search for Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude 1/ c is an approximation scheme for the following problems in the Euclidean plane: TSP with random inputs, Steiner tree with random inputs, uniform facility location (with worst case inputs), and bicriteria k-median (also with worst case inputs). T...

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

Geometric Facility Location under Continuous Motion Bounded-Velocity Approximations to the Mobile Euclidean k-Centre and k-Median Problems

The traditional problems of facility location are defined statically; a set (or multiset) of n points is given as input, corresponding to the positions of clients, and a solution is returned consisting of set of k points, corresponding to the positions of facilities, that optimizes some objective function of the input set. In the k-centre problem, the objective is to select k points for locatin...