41,747 research outputs found
A Tool Based Edge Server Selection Technique using Spatial Data Structure
Space partitioning is the process of dividing a Euclidean space into a non-overlapping regions. Kdimensional tree is such space-partitioning data structure for partitioning a Euclidean plane like the surface of earth. This paper describes a tool-based logically partitioning technique of earth surface using K-dimensional tree to segregate the edge servers over the earth surface into a nonoverlapping regions for the particular Content Delivery Network. Consequently selecting an edge server based on Least Response Time lo ad balancing algorithm is introduced to improve end-user response time and fault tolerance of the host server
Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition
We provide efficient constant factor approximation algorithms for the
problems of finding a hierarchical clustering of a point set in any metric
space, minimizing the sum of minimimum spanning tree lengths within each
cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of
cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can
also be used to provide a pants decomposition, that is, a set of disjoint
simple closed curves partitioning the plane minus the input points into subsets
with exactly three boundary components, with approximately minimum total
length. In the Euclidean case, these curves are squares; in the hyperbolic
case, they combine our Euclidean square pants decomposition with our tree
clustering method for general metric spaces.Comment: 22 pages, 14 figures. This version replaces the proof of what is now
Lemma 5.2, as the previous proof was erroneou
Popularity on the 3D-Euclidean Stable Roommates
We study the 3D-Euclidean Multidimensional Stable Roommates problem, which
asks whether a given set of agents with a location in
3-dimensional Euclidean space can be partitioned into disjoint subsets with for each such that
is (strictly) popular, where is the room size. A partitioning is popular if
there does not exist another partitioning in which more agents are better off
than worse off. Computing a popular partition in a stable roommates game is
NP-hard, even if the preferences are strict. The preference of an agent solely
depends on the distance to its roommates. An agent prefers to be in a room
where the sum of the distances to its roommates is small. We show that
determining the existence of a strictly popular outcome in a 3D-Euclidean
Multidimensional Stable Roommates game with room size is co-NP-hard.Comment: 27 pages, 23 figure
Spanners for Geometric Intersection Graphs
Efficient algorithms are presented for constructing spanners in geometric
intersection graphs. For a unit ball graph in R^k, a (1+\epsilon)-spanner is
obtained using efficient partitioning of the space into hypercubes and solving
bichromatic closest pair problems. The spanner construction has almost
equivalent complexity to the construction of Euclidean minimum spanning trees.
The results are extended to arbitrary ball graphs with a sub-quadratic running
time.
For unit ball graphs, the spanners have a small separator decomposition which
can be used to obtain efficient algorithms for approximating proximity problems
like diameter and distance queries. The results on compressed quadtrees,
geometric graph separators, and diameter approximation might be of independent
interest.Comment: 16 pages, 5 figures, Late
Markov Chain Methods For Analyzing Complex Transport Networks
We have developed a steady state theory of complex transport networks used to
model the flow of commodity, information, viruses, opinions, or traffic. Our
approach is based on the use of the Markov chains defined on the graph
representations of transport networks allowing for the effective network
design, network performance evaluation, embedding, partitioning, and network
fault tolerance analysis. Random walks embed graphs into Euclidean space in
which distances and angles acquire a clear statistical interpretation. Being
defined on the dual graph representations of transport networks random walks
describe the equilibrium configurations of not random commodity flows on
primary graphs. This theory unifies many network concepts into one framework
and can also be elegantly extended to describe networks represented by directed
graphs and multiple interacting networks.Comment: 26 pages, 4 figure
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