  In this paper we present new algorithmic solutions for several constrained
geometric server placement problems. We consider the problems of computing the
1-center and obnoxious 1-center of a set of line segments, constrained to lie
on a line segment, and the problem of computing the K-median of a set of
points, constrained to lie on a line. The presented algorithms have
applications in many types of distributed systems, as well as in various fields
which make use of distributed systems for running some of their applications
(like chemistry, metallurgy, physics, etc.).
