Approximation algorithms for the geometric covering salesman problem

Approximation Algorithms for the Geometric Covering Salesman Problem

We introduce a geometric version of the Covering Salesman Problem: Each of the n salesman's clients speciies a neighborhood in which they are willing to meet the salesman. Identifying a tour of minimum length that visits all neighborhoods is an NP-hard problem, since it is a generalization of the Traveling Salesman Problem. We present simple heuristic procedures for constructing tours, for a va...

Approximation algorithms for the traveling salesman problem

We first prove that the minimum and maximum traveling salesman problems, their metric versions as well as some versions defined on parameterized triangle inequalities (called sharpened and relaxed metric traveling salesman) are all equi-approximable under an approximation measure, called differential-approximation ratio, that measures how the value of an approximate solution is placed in the in...

Approximation algorithms for the covering Steiner problem

The Generalized Covering Salesman Problem

Given a graph ( , ) G N E  , the Covering Salesman Problem (CSP) is to identify the minimum length tour “covering” all the nodes. More specifically, it seeks the minimum length tour visiting a subset of the nodes in N such that each node i not on the tour is within a predetermined distance di of a node on the tour. In this paper, we define and develop a generalized version of the CSP, and refe...

Approximation Algorithms for Geometric Covering Problems for Disks and Squares

Geometric covering is a well-studied topic in computational geometry. We study three covering problems: Disjoint Unit-Disk Cover, Depth-(≤ K) Packing and Red-Blue UnitSquare Cover. In the Disjoint Unit-Disk Cover problem, we are given a point set and want to cover the maximum number of points using disjoint unit disks. We prove that the problem is NP-complete and give a polynomial-time approxim...