397 research outputs found
On the Monadic Second-Order Transduction Hierarchy
We compare classes of finite relational structures via monadic second-order
transductions. More precisely, we study the preorder where we set C \subseteq K
if, and only if, there exists a transduction {\tau} such that
C\subseteq{\tau}(K). If we only consider classes of incidence structures we can
completely describe the resulting hierarchy. It is linear of order type
{\omega}+3. Each level can be characterised in terms of a suitable variant of
tree-width. Canonical representatives of the various levels are: the class of
all trees of height n, for each n \in N, of all paths, of all trees, and of all
grids
Are there any good digraph width measures?
Several different measures for digraph width have appeared in the last few
years. However, none of them shares all the "nice" properties of treewidth:
First, being \emph{algorithmically useful} i.e. admitting polynomial-time
algorithms for all \MS1-definable problems on digraphs of bounded width. And,
second, having nice \emph{structural properties} i.e. being monotone under
taking subdigraphs and some form of arc contractions. As for the former,
(undirected) \MS1 seems to be the least common denominator of all reasonably
expressive logical languages on digraphs that can speak about the edge/arc
relation on the vertex set.The latter property is a necessary condition for a
width measure to be characterizable by some version of the cops-and-robber game
characterizing the ordinary treewidth. Our main result is that \emph{any
reasonable} algorithmically useful and structurally nice digraph measure cannot
be substantially different from the treewidth of the underlying undirected
graph. Moreover, we introduce \emph{directed topological minors} and argue that
they are the weakest useful notion of minors for digraphs
Proofs of partial correctness for attribute grammars with applications to recursive procedures and logic programming
AbstractAn extension of the inductive assertion method allowing one to prove the partial correctness of an attribute grammar w.r.t. a specification is presented. It is complete in an abstract sense. It is also shown that the semantics of systems of recursive imperative procedures or of recursive applicative procedures computed with call-by-value or call-by-name can be expressed by an attribute grammar associating attributes with the nodes of the so-called trees of calls. Hence the proof methods for the partial correctness of attribute grammars can be applied to these recursive procedures. We show also how the proof method can be applied in logic programming
A Natural Generalization of Bounded Tree-Width and Bounded Clique-Width
We investigate a new width parameter, the fusion-width of a graph. It is a
natural generalization of the tree-width, yet strong enough that not only
graphs of bounded tree-width, but also graphs of bounded clique-width,
trivially have bounded fusion-width. In particular, there is no exponential
growth between tree-width and fusion-width, as is the case between tree-width
and clique-width. The new parameter gives a good intuition about the
relationship between tree-width and clique-width.Comment: To appear in the proceedings of Latin 2014. Springer LNCS 839
Between Treewidth and Clique-width
Many hard graph problems can be solved efficiently when restricted to graphs
of bounded treewidth, and more generally to graphs of bounded clique-width. But
there is a price to be paid for this generality, exemplified by the four
problems MaxCut, Graph Coloring, Hamiltonian Cycle and Edge Dominating Set that
are all FPT parameterized by treewidth but none of which can be FPT
parameterized by clique-width unless FPT = W[1], as shown by Fomin et al [7,
8]. We therefore seek a structural graph parameter that shares some of the
generality of clique-width without paying this price. Based on splits, branch
decompositions and the work of Vatshelle [18] on Maximum Matching-width, we
consider the graph parameter sm-width which lies between treewidth and
clique-width. Some graph classes of unbounded treewidth, like
distance-hereditary graphs, have bounded sm-width. We show that MaxCut, Graph
Coloring, Hamiltonian Cycle and Edge Dominating Set are all FPT parameterized
by sm-width
Compact Labelings For Efficient First-Order Model-Checking
We consider graph properties that can be checked from labels, i.e., bit
sequences, of logarithmic length attached to vertices. We prove that there
exists such a labeling for checking a first-order formula with free set
variables in the graphs of every class that is \emph{nicely locally
cwd-decomposable}. This notion generalizes that of a \emph{nicely locally
tree-decomposable} class. The graphs of such classes can be covered by graphs
of bounded \emph{clique-width} with limited overlaps. We also consider such
labelings for \emph{bounded} first-order formulas on graph classes of
\emph{bounded expansion}. Some of these results are extended to counting
queries
Convex Independence in Permutation Graphs
A set C of vertices of a graph is P_3-convex if every vertex outside C has at
most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest
P_3-convex set that contains A. A set M is convexly independent if for every
vertex x \in M, x \notin \sigma(M-x). We show that the maximal number of
vertices that a convexly independent set in a permutation graph can have, can
be computed in polynomial time
Parameterized Edge Hamiltonicity
We study the parameterized complexity of the classical Edge Hamiltonian Path
problem and give several fixed-parameter tractability results. First, we settle
an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT
parameterized by vertex cover, and that it also admits a cubic kernel. We then
show fixed-parameter tractability even for a generalization of the problem to
arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set.
We also consider the problem parameterized by treewidth or clique-width.
Surprisingly, we show that the problem is FPT for both of these standard
parameters, in contrast to its vertex version, which is W-hard for
clique-width. Our technique, which may be of independent interest, relies on a
structural characterization of clique-width in terms of treewidth and complete
bipartite subgraphs due to Gurski and Wanke
A SAT Approach to Clique-Width
Clique-width is a graph invariant that has been widely studied in
combinatorics and computer science. However, computing the clique-width of a
graph is an intricate problem, the exact clique-width is not known even for
very small graphs. We present a new method for computing the clique-width of
graphs based on an encoding to propositional satisfiability (SAT) which is then
evaluated by a SAT solver. Our encoding is based on a reformulation of
clique-width in terms of partitions that utilizes an efficient encoding of
cardinality constraints. Our SAT-based method is the first to discover the
exact clique-width of various small graphs, including famous graphs from the
literature as well as random graphs of various density. With our method we
determined the smallest graphs that require a small pre-described clique-width.Comment: proofs in section 3 updated, results remain unchange
EFFETS DES TRAITEMENTS THERMIQUES SUR LES PROPRIETES ELECTRIQUES DES CELLULES SOLAIRES A BASE DE SILICIUM POLYCRISTALLIN
On a étudié l'effet de recuits à haute température sur les caractéristiques électriques à l'obscurité et sous éclairement de cellules solaires à base de silicium polycristallin dont la jonction était préparée à froid par incrustation ionique et recuit par laser pulsé. Dans certains cas des dégradations notables sont observées pour des recuits à 900°C
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