21 research outputs found
Structural characterization of some problems on circle and interval graphs
A graph is circle if there is a family of chords in a circle such that two
vertices are adjacent if the corresponding chords cross each other. There are
diverse characterizations of circle graphs, many of them using the notions of
local complementation or split decomposition. However, there are no known
structural characterization by minimal forbidden induced subgraphs for circle
graphs. In this thesis, we give a characterization by forbidden induced
subgraphs of circle graphs within split graphs. A -matrix has the
consecutive-ones property (C1P) for the rows if there is a permutation of its
columns such that the 's in each row appear consecutively. In this thesis,
we develop characterizations by forbidden subconfigurations of -matrices
with the C1P for which the rows are -colorable under a certain adjacency
relationship, and we characterize structurally some auxiliary circle graph
subclasses that arise from these special matrices. Given a graph class , a
-completion of a graph is a graph such
that belongs to . A -completion of is minimal if does not belong to for every proper subset of . A
-completion of is minimum if for every -completion of , the cardinal of is less than or equal to the cardinal
of . In this thesis, we study the problem of completing minimally to obtain
a proper interval graph when the input is an interval graph. We find necessary
conditions that characterize a minimal completion in this particular case, and
we leave some conjectures for the future.Comment: PhD Thesis, joint supervision Universidad de Buenos
Aires-Universit\'e Paris-Nord. Dissertation took place on March 30th 202
2-nested matrices: towards understanding the structure of circle graphs
A -matrix has the consecutive-ones property (C1P) if its columns can
be permuted to make the 's in each row appear consecutively. This property
was characterised in terms of forbidden submatrices by Tucker in 1972. Several
graph classes were characterised by means of this property, including interval
graphs and strongly chordal digraphs. In this work, we define and characterise
2-nested matrices, which are -matrices with a variant of the C1P and for
which there is also certain assignment of one of two colors to each block of
consecutive 's in each row. The characterization of 2-nested matrices in the
present work is of key importance to characterise split graphs that are also
circle by minimal forbidden induced subgraphs.Comment: 46 pages, 15 figure
Data-graph repairs: the preferred approach
Repairing inconsistent knowledge bases is a task that has been assessed, with
great advances over several decades, from within the knowledge representation
and reasoning and the database theory communities. As information becomes more
complex and interconnected, new types of repositories, representation languages
and semantics are developed in order to be able to query and reason about it.
Graph databases provide an effective way to represent relationships among data,
and allow processing and querying these connections efficiently. In this work,
we focus on the problem of computing preferred (subset and superset) repairs
for graph databases with data values, using a notion of consistency based on a
set of Reg-GXPath expressions as integrity constraints. Specifically, we study
the problem of computing preferred repairs based on two different preference
criteria, one based on weights and the other based on multisets, showing that
in most cases it is possible to retain the same computational complexity as in
the case where no preference criterion is available for exploitation.Comment: arXiv admin note: text overlap with arXiv:2206.0750
Edge deletion to tree-like graph classes
For a fixed property (graph class) , given a graph and an integer
, the -deletion problem consists in deciding if we can turn into a
graph with the property by deleting at most edges of . The
-deletion problem is known to be NP-hard for most of the well-studied
graph classes (such as chordal, interval, bipartite, planar, comparability and
permutation graphs, among others), with the notable exception of trees.
Motivated by this fact, in this work we study the deletion problem for some
classes close to trees. We obtain NP-hardness results for several classes of
sparse graphs, for which we prove that deletion is hard even when the input is
a bipartite graph. In addition, we give sufficient structural conditions for
the graph class for NP-hardness. In the case of deletion to cactus, we
show that the problem becomes tractable when the input is chordal, and we give
polynomial-time algorithms for quasi-threshold graphs.Comment: 12 pages, no figure
Unified Foundations of Team Semantics via Semirings
Semiring semantics for first-order logic provides a way to trace how facts
represented by a model are used to deduce satisfaction of a formula. Team
semantics is a framework for studying logics of dependence and independence in
diverse contexts such as databases, quantum mechanics, and statistics by
extending first-order logic with atoms that describe dependencies between
variables. Combining these two, we propose a unifying approach for analysing
the concepts of dependence and independence via a novel semiring team
semantics, which subsumes all the previously considered variants for
first-order team semantics. In particular, we study the preservation of
satisfaction of dependencies and formulae between different semirings. In
addition we create links to reasoning tasks such as provenance, counting, and
repairs
On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
A (0, 1)-matrix has the Consecutive Ones Property (C1P) for the rows if there is a permutation of its columns such that the ones in each row appear consecutively. We say a (0, 1)-matrix is nested if it has the consecutive ones property for the rows (C1P) and every two rows are either disjoint or nested. We say a (0, 1)-matrix is 2-nested if it has the C1P and admits a partition of its rows into two sets such that the submatrix induced by each of these sets is nested. We say a split graph G with split partition (K, S) is nested (resp. 2-nested) if the matrix A(S, K) which indicates the adjacency between vertices in S and K is nested (resp. 2-nested). In this work, we characterize nested and 2-nested matrices by minimal forbidden submatrices. This characterization leads to a minimal forbidden induced subgraph characterization of these graph classes, which are superclasses of threshold graphs and subclasses of split and circle graphs.Fil: Pardal, Nina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Duran, Guillermo Alfredo. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Safe, Martin Dario. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Forbidden induced subgraph characterization of circle graphs within split graphs
A graph is circle if its vertices are in correspondence with a family of
chords in a circle in such a way that every two distinct vertices are adjacent
if and only if the corresponding chords have nonempty intersection. Even though
there are diverse characterizations of circle graphs, a structural
characterization by minimal forbidden induced subgraphs for the entire class of
circle graphs is not known, not even restricted to split graphs (which are the
graphs whose vertex set can be partitioned into a clique and a stable set). In
this work, we give a characterization by minimal forbidden induced subgraphs of
circle graphs, restricted to split graphs.Comment: 59 pages, 15 figure
An epistemic approach to model uncertainty in data-graphs
Graph databases are becoming widely successful as data models that allow to
effectively represent and process complex relationships among various types of
data. As with any other type of data repository, graph databases may suffer
from errors and discrepancies with respect to the real-world data they intend
to represent. In this work we explore the notion of probabilistic unclean graph
databases, previously proposed for relational databases, in order to capture
the idea that the observed (unclean) graph database is actually the noisy
version of a clean one that correctly models the world but that we know
partially. As the factors that may be involved in the observation can be many,
e.g, all different types of clerical errors or unintended transformations of
the data, we assume a probabilistic model that describes the distribution over
all possible ways in which the clean (uncertain) database could have been
polluted. Based on this model we define two computational problems: data
cleaning and probabilistic query answering and study for both of them their
corresponding complexity when considering that the transformation of the
database can be caused by either removing (subset) or adding (superset) nodes
and edges.Comment: 25 pages, 3 figure
On the complexity of finding set repairs for data-graphs
In the deeply interconnected world we live in, pieces of information link
domains all around us. As graph databases embrace effectively relationships
among data and allow processing and querying these connections efficiently,
they are rapidly becoming a popular platform for storage that supports a wide
range of domains and applications. As in the relational case, it is expected
that data preserves a set of integrity constraints that define the semantic
structure of the world it represents. When a database does not satisfy its
integrity constraints, a possible approach is to search for a 'similar'
database that does satisfy the constraints, also known as a repair. In this
work, we study the problem of computing subset and superset repairs for graph
databases with data values using a notion of consistency based on a set of
Reg-GXPath expressions as integrity constraints. We show that for positive
fragments of Reg-GXPath these problems admit a polynomial-time algorithm, while
the full expressive power of the language renders them intractable.Comment: 35 pages , including Appendi
Subspecialty training in Europe:a report by the European Network of Young Gynaecological Oncologists
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