 
Summary: APPROXIMATION ALGORITHMS FOR THE
GEOMETRIC COVERING SALESMAN PROBLEM
Esther M. Arkin y
Department of Applied Mathematics and Statistics
SUNY Stony Brook
Stony Brook, NY 117943600
Email: estie@ams.sunysb.edu
Refael Hassin
Department of Statistics and Operations Research
School of Mathematical Sciences
TelAviv University
TelAviv 69978, Israel
Email: hassin@math.tau.ac.il
August 25, 1995
Abstract
We introduce a geometric version of the Covering Salesman Problem: Each of the n salesman's
clients specifies a neighborhood in which they are willing to meet the salesman. Identifying a tour
of minimum length that visits all neighborhoods is an NPhard problem, since it is a generalization
of the Traveling Salesman Problem. We present simple heuristic procedures for constructing tours,
for a variety of neighborhood types, whose length is guaranteed to be within a constant factor
