6,609 research outputs found
Fixed-parameter tractability, definability, and model checking
In this article, we study parameterized complexity theory from the
perspective of logic, or more specifically, descriptive complexity theory.
We propose to consider parameterized model-checking problems for various
fragments of first-order logic as generic parameterized problems and show how
this approach can be useful in studying both fixed-parameter tractability and
intractability. For example, we establish the equivalence between the
model-checking for existential first-order logic, the homomorphism problem for
relational structures, and the substructure isomorphism problem. Our main
tractability result shows that model-checking for first-order formulas is
fixed-parameter tractable when restricted to a class of input structures with
an excluded minor. On the intractability side, for every t >= 0 we prove an
equivalence between model-checking for first-order formulas with t quantifier
alternations and the parameterized halting problem for alternating Turing
machines with t alternations. We discuss the close connection between this
alternation hierarchy and Downey and Fellows' W-hierarchy.
On a more abstract level, we consider two forms of definability, called Fagin
definability and slicewise definability, that are appropriate for describing
parameterized problems. We give a characterization of the class FPT of all
fixed-parameter tractable problems in terms of slicewise definability in finite
variable least fixed-point logic, which is reminiscent of the Immerman-Vardi
Theorem characterizing the class PTIME in terms of definability in least
fixed-point logic.Comment: To appear in SIAM Journal on Computin
A link density clustering algorithm based on automatically selecting density peaks for overlapping community detection
Peer reviewedPostprin
Data Management and Mining in Astrophysical Databases
We analyse the issues involved in the management and mining of astrophysical
data. The traditional approach to data management in the astrophysical field is
not able to keep up with the increasing size of the data gathered by modern
detectors. An essential role in the astrophysical research will be assumed by
automatic tools for information extraction from large datasets, i.e. data
mining techniques, such as clustering and classification algorithms. This asks
for an approach to data management based on data warehousing, emphasizing the
efficiency and simplicity of data access; efficiency is obtained using
multidimensional access methods and simplicity is achieved by properly handling
metadata. Clustering and classification techniques, on large datasets, pose
additional requirements: computational and memory scalability with respect to
the data size, interpretability and objectivity of clustering or classification
results. In this study we address some possible solutions.Comment: 10 pages, Late
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