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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.).
We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional hypercubes. It
Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A times B$ so that any point of $A cup B$ appears in at most one
Consider a unit interval $[0,1]$ in which $n$ points arrive one-by-one independently and uniformly at random. On arrival of a point, the problem is to immediately and irrevocably color it in ${+1,-1}$ while ensuring that every interval $[a,b] subsete
Let $mathscr O$ be a set of $n$ disjoint obstacles in $mathbb{R}^2$, $mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $mathscr M$, respectively. Given a point $p$ in ${R}^2$, we sa
We study how to design edge server placement and server scheduling policies under workload uncertainty for 5G networks. We introduce a new metric called resource pooling factor to handle unexpected workload bursts. Maximizing this metric offers a str