35,907 research outputs found
Improvements on the k-center problem for uncertain data
In real applications, there are situations where we need to model some
problems based on uncertain data. This leads us to define an uncertain model
for some classical geometric optimization problems and propose algorithms to
solve them. In this paper, we study the -center problem, for uncertain
input. In our setting, each uncertain point is located independently from
other points in one of several possible locations in a metric space with metric , with specified probabilities
and the goal is to compute -centers that minimize the
following expected cost here
is the probability space of all realizations of given uncertain points and
In restricted assigned version of this problem, an assignment is given for any choice of centers and the
goal is to minimize In unrestricted version, the
assignment is not specified and the goal is to compute centers
and an assignment that minimize the above expected
cost.
We give several improved constant approximation factor algorithms for the
assigned versions of this problem in a Euclidean space and in a general metric
space. Our results significantly improve the results of \cite{guh} and
generalize the results of \cite{wang} to any dimension. Our approach is to
replace a certain center point for each uncertain point and study the
properties of these certain points. The proposed algorithms are efficient and
simple to implement
A Short Survey on Data Clustering Algorithms
With rapidly increasing data, clustering algorithms are important tools for
data analytics in modern research. They have been successfully applied to a
wide range of domains; for instance, bioinformatics, speech recognition, and
financial analysis. Formally speaking, given a set of data instances, a
clustering algorithm is expected to divide the set of data instances into the
subsets which maximize the intra-subset similarity and inter-subset
dissimilarity, where a similarity measure is defined beforehand. In this work,
the state-of-the-arts clustering algorithms are reviewed from design concept to
methodology; Different clustering paradigms are discussed. Advanced clustering
algorithms are also discussed. After that, the existing clustering evaluation
metrics are reviewed. A summary with future insights is provided at the end
Graph Summarization
The continuous and rapid growth of highly interconnected datasets, which are
both voluminous and complex, calls for the development of adequate processing
and analytical techniques. One method for condensing and simplifying such
datasets is graph summarization. It denotes a series of application-specific
algorithms designed to transform graphs into more compact representations while
preserving structural patterns, query answers, or specific property
distributions. As this problem is common to several areas studying graph
topologies, different approaches, such as clustering, compression, sampling, or
influence detection, have been proposed, primarily based on statistical and
optimization methods. The focus of our chapter is to pinpoint the main graph
summarization methods, but especially to focus on the most recent approaches
and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie
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