Reverse 2-median problem on trees

The k-Median Problem for Directed Trees

An Efficient Algorithm for Reverse 2-median Problem on A Cycle

Location problems exist extensively in the real world and they mainly deal with finding optimal locations for facilities. However, the reverse location problem is also often met in practice, in which the facilities may already exist in a network and cannot be moved to a new place, the task is to improve the network within a given budget such that the improved network works as efficient as possi...

Efficient Algorithms for Two Generalized 2-Median Problems on Trees

The p-median problem on a tree T is to find a set S of p vertices on T that minimize the sum of distances from T’s vertices to S. For this problem, Tamir [14] had an O(pn)-time algorithm, while Gavish and Sridhar [6] had an O(nlog n)-time algorithm for the case of p=2. In this paper, we study two generalizations of the 2-median problem, which are obtained by imposing constraints on a 2-median: ...

The Reverse Greedy Algorithm for the Metric K-Median Problem

The Reverse Greedy algorithm (RGREEDY) for the k-median problem works as follows. It starts by placing facilities on all nodes. At each step, it removes a facility to minimize the total distance to the remaining facilities. It stops when k facilities remain. We prove that, if the distance function is metric, then the approximation ratio of RGREEDY is between (logn/ log logn) and O(logn).  2005...

On the DCJ Median Problem

As many whole genomes are sequenced, comparative genomics is moving from pairwise comparisons to multiway comparisons framed within a phylogenetic tree. A central problem in this process is the inference of data for internal nodes of the tree from data given at the leaves.When phrased as an optimization problem, this problem reduces to computing a median of three genomes under the operations (e...