3,705 research outputs found
On -Guarding Thin Orthogonal Polygons
Guarding a polygon with few guards is an old and well-studied problem in
computational geometry. Here we consider the following variant: We assume that
the polygon is orthogonal and thin in some sense, and we consider a point
to guard a point if and only if the minimum axis-aligned rectangle spanned
by and is inside the polygon. A simple proof shows that this problem is
NP-hard on orthogonal polygons with holes, even if the polygon is thin. If
there are no holes, then a thin polygon becomes a tree polygon in the sense
that the so-called dual graph of the polygon is a tree. It was known that
finding the minimum set of -guards is polynomial for tree polygons, but the
run-time was . We show here that with a different approach
the running time becomes linear, answering a question posed by Biedl et al.
(SoCG 2011). Furthermore, the approach is much more general, allowing to
specify subsets of points to guard and guards to use, and it generalizes to
polygons with holes or thickness , becoming fixed-parameter tractable in
.Comment: 18 page
Thinness of product graphs
The thinness of a graph is a width parameter that generalizes some properties
of interval graphs, which are exactly the graphs of thinness one. Many
NP-complete problems can be solved in polynomial time for graphs with bounded
thinness, given a suitable representation of the graph. In this paper we study
the thinness and its variations of graph products. We show that the thinness
behaves "well" in general for products, in the sense that for most of the graph
products defined in the literature, the thinness of the product of two graphs
is bounded by a function (typically product or sum) of their thinness, or of
the thinness of one of them and the size of the other. We also show for some
cases the non-existence of such a function.Comment: 45 page
The ergodic theory of hyperbolic groups
These notes are a self-contained introduction to the use of dynamical and
probabilistic methods in the study of hyperbolic groups. Most of this material
is standard; however some of the proofs given are new, and some results are
proved in greater generality than have appeared in the literature. These notes
originated in a minicourse given at a workshop in Melbourne, July 11-15 2011.Comment: 37 pages, 5 figures; incorporates referee's comment
Definability equals recognizability for graphs of bounded treewidth
We prove a conjecture of Courcelle, which states that a graph property is
definable in MSO with modular counting predicates on graphs of constant
treewidth if, and only if it is recognizable in the following sense:
constant-width tree decompositions of graphs satisfying the property can be
recognized by tree automata. While the forward implication is a classic fact
known as Courcelle's theorem, the converse direction remained openComment: 21 pages, an extended abstract will appear in the proceedings of LICS
201
Precedence thinness in graphs
Interval and proper interval graphs are very well-known graph classes, for
which there is a wide literature. As a consequence, some generalizations of
interval graphs have been proposed, in which graphs in general are expressed in
terms of interval graphs, by splitting the graph in some special way.
As a recent example of such an approach, the classes of -thin and proper
-thin graphs have been introduced generalizing interval and proper interval
graphs, respectively. The complexity of the recognition of each of these
classes is still open, even for fixed .
In this work, we introduce a subclass of -thin graphs (resp. proper
-thin graphs), called precedence -thin graphs (resp. precedence proper
-thin graphs). Concerning partitioned precedence -thin graphs, we present
a polynomial time recognition algorithm based on -trees. With respect to
partitioned precedence proper -thin graphs, we prove that the related
recognition problem is \NP-complete for an arbitrary and polynomial-time
solvable when is fixed. Moreover, we present a characterization for these
classes based on threshold graphs.Comment: 33 page
A Kite Simulation System using Position-based Method
Thesis (Master of Information Scienc)--University of Tsukuba, no. 37782, 2017.3.2
Non-normal real estate return distributions by property type in the U.K.
Investment risk models with infinite variance provide a better description of distributions of individual property returns in the IPD database over the period 1981 to 2003 than Normally distributed risk models, which mirrors results in the U.S. and Australia using identical methodology. Real estate investment risk is heteroscedastic, but the Characteristic Exponent of the investment risk function is constant across time yet may vary by property type. Asset diversification is far less effective at reducing the impact of non-systematic investment risk on real estate portfolios than in the case of assets with Normally distributed investment risk. Multi-risk factor portfolio allocation models based on measures of investment codependence from finite-variance statistics are ineffectual in the real estate context
Eigenvaluations
We study the dynamics in C^2 of superattracting fixed point germs and of
polynomial maps near infinity. In both cases we show that the asymptotic
attraction rate is a quadratic integer, and construct a plurisubharmonic
function with the adequate invariance property. This is done by finding an
infinitely near point at which the map becomes rigid: the critical set is
contained in a totally invariant set with normal crossings. We locate this
infinitely near point through the induced action of the dynamics on a space of
valuations. This space carries an real-tree structure and conveniently encodes
local data: an infinitely near point corresponds to a open subset of the tree.
The action respects the tree structure and admits a fixed point--or
eigenvaluation--which is attracting in a certain sense. A suitable basin of
attraction corresponds to the desired infinitely near point.Comment: 48 pages, 2 figures, To appear in Annales de l'EN
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