Line-Constrained Geometric Server Placement

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.).

Clustering, Encoding and Diameter Computation Algorithms for Multidimensional Data

In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We also consider two string (1D data) processing problems, regarding an optimal encoding method and the computation of the number of occurrences of a substring within a string generated by a grammar. The algorithms have been thoroughly analyzed from a theoretical point of view and some of them have also been evaluated experimentally.