On Variant Clique Problems and their Applications
Date
2018-11-13
Authors
Xiao, Zhuoli
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Abstract
Clique-based problems, often called cluster problems, receive more and more attention in computer science as well as many of its application areas. Clique-based problems
can be used to model a number of real-world problems and with this comes the motivation
to provide algorithmic solutions for them. While one can nd quite a lot
of literature on clique-based problems in general, only for few speci c versions exact
algorithmic solutions are discussed in detail. In this project, we survey such cliquebased
problems from the literature, investigate their properties, their exact algorithms
and respective running times, and discuss some of their applications.
In particular, in depth we consider the two NP-complete clique-based problems Edge
Clique Partition and Edge Clique Cover. For their natural parameterizations,
k-Edge Clique Partition and k-Edge Clique Cover, we present xedparameter
algorithms based on results in the literature, suggest some pre-processing
rules (also called reduction rules) that we have not seen in the literature, as well as
discuss some of their current and potential real-world applications.
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Keywords
Cliques, Clusters, Parameterized Complexity, NP-Complete, Edge Clique Partition, Edge Clique Cover, Applications, Graph Theory