Efficient algorithms for center problems in cactus networks
Theoretical Computer Science
New Upper Bounds on Continuous Tree Edge-Partition Problem
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
An optimal algorithm for the maximum-density path in a tree
Information Processing Letters
The pos/neg-weighted 1-median problem on tree graphs with subtree-shaped customers
Theoretical Computer Science
A new template for solving p-median problems for trees in sub-quadratic time
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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Operations Research is the application of scientific methods, especially mathematical and statistical ones, to problems of making decisions. From the huge variety of real life applications, this thesis focuses on a particular class of problems for which the placement of certain resources is in question. These tasks are referred collectively as facility location problems. This dissertation is about algorithms to solve a fundamental problem in facility location, the k-median problem. The mathematical object used here in modeling the resources and their interactions with the environment is a tree. Many other formulations are used in practice with the k-median problem, but the case of trees is special because, (i) the formulation is very simple, (ii) problems can be solved efficiently, (iii) efficient algorithms for problems in trees can be used to derive approximate solutions for general networks (Tamir (102]), and (iv) efficient algorithms for k-median problems in trees could lead to specific k-median algorithms for classes of graphs less studied, such as the graphs with bounded tree-width. Using simple techniques from computational geometry, we give the first k-median algorithm sub-quadratic in the size of the tree when k is fixed, for arbitrary trees. In the introduction, we give an overview of the main results known about the k-median problem in general. The main ideas behind our approach are also illustrated. In Chapter 2 we present a decomposition of trees that is central to our methods. In Chapter 3 we describe our approach for solving the k-median problem in trees and we give simplified algorithms for three particular cases, the 3-median problem, the k-median problem in directed trees, and the k-median problem in balanced binary trees. The following two chapters discuss two generalizations of the k-median problem, the k-median problem with positive and negative weights and the collection depots problem.