44,338 research outputs found
A PTAS for the minimum dominating set problem in unit disk graphs
We present a polynomial-time approximation scheme (PTAS) for the minimum dominating set problem in unit disk graphs. In contrast to previously known approximation schemes for the minimum dominating set problem on unit disk graphs, our approach does not assume a geometric representation of the vertices (specifying the positions of the disks in the plane) to be given as part of the input. \u
Analysis of a non-minimum phase acoustic beamformer
The two input Griffiths-Jim acoustic beamformer is analysed in the frequency domain using
a Wiener type formulation. Unlike previous solutions the approach here is to look at the
problem of non-minimum phase acoustic transfer functions which are encountered in many
real filtering problems. The polynomial transfer function approach gives an elegant way of
obtaining the frequency response of the beamformer and gives new insight to the problem
in general
Graph Isomorphism for unit square graphs
In the past decades for more and more graph classes the Graph Isomorphism
Problem was shown to be solvable in polynomial time. An interesting family of
graph classes arises from intersection graphs of geometric objects. In this
work we show that the Graph Isomorphism Problem for unit square graphs,
intersection graphs of axis-parallel unit squares in the plane, can be solved
in polynomial time. Since the recognition problem for this class of graphs is
NP-hard we can not rely on standard techniques for geometric graphs based on
constructing a canonical realization. Instead, we develop new techniques which
combine structural insights into the class of unit square graphs with
understanding of the automorphism group of such graphs. For the latter we
introduce a generalization of bounded degree graphs which is used to capture
the main structure of unit square graphs. Using group theoretic algorithms we
obtain sufficient information to solve the isomorphism problem for unit square
graphs.Comment: 31 pages, 6 figure
Recognising Multidimensional Euclidean Preferences
Euclidean preferences are a widely studied preference model, in which
decision makers and alternatives are embedded in d-dimensional Euclidean space.
Decision makers prefer those alternatives closer to them. This model, also
known as multidimensional unfolding, has applications in economics,
psychometrics, marketing, and many other fields. We study the problem of
deciding whether a given preference profile is d-Euclidean. For the
one-dimensional case, polynomial-time algorithms are known. We show that, in
contrast, for every other fixed dimension d > 1, the recognition problem is
equivalent to the existential theory of the reals (ETR), and so in particular
NP-hard. We further show that some Euclidean preference profiles require
exponentially many bits in order to specify any Euclidean embedding, and prove
that the domain of d-Euclidean preferences does not admit a finite forbidden
minor characterisation for any d > 1. We also study dichotomous preferencesand
the behaviour of other metrics, and survey a variety of related work.Comment: 17 page
Large Scale SfM with the Distributed Camera Model
We introduce the distributed camera model, a novel model for
Structure-from-Motion (SfM). This model describes image observations in terms
of light rays with ray origins and directions rather than pixels. As such, the
proposed model is capable of describing a single camera or multiple cameras
simultaneously as the collection of all light rays observed. We show how the
distributed camera model is a generalization of the standard camera model and
describe a general formulation and solution to the absolute camera pose problem
that works for standard or distributed cameras. The proposed method computes a
solution that is up to 8 times more efficient and robust to rotation
singularities in comparison with gDLS. Finally, this method is used in an novel
large-scale incremental SfM pipeline where distributed cameras are accurately
and robustly merged together. This pipeline is a direct generalization of
traditional incremental SfM; however, instead of incrementally adding one
camera at a time to grow the reconstruction the reconstruction is grown by
adding a distributed camera. Our pipeline produces highly accurate
reconstructions efficiently by avoiding the need for many bundle adjustment
iterations and is capable of computing a 3D model of Rome from over 15,000
images in just 22 minutes.Comment: Published at 2016 3DV Conferenc
On the structure of (pan, even hole)-free graphs
A hole is a chordless cycle with at least four vertices. A pan is a graph
which consists of a hole and a single vertex with precisely one neighbor on the
hole. An even hole is a hole with an even number of vertices. We prove that a
(pan, even hole)-free graph can be decomposed by clique cutsets into
essentially unit circular-arc graphs. This structure theorem is the basis of
our -time certifying algorithm for recognizing (pan, even hole)-free
graphs and for our -time algorithm to optimally color them.
Using this structure theorem, we show that the tree-width of a (pan, even
hole)-free graph is at most 1.5 times the clique number minus 1, and thus the
chromatic number is at most 1.5 times the clique number.Comment: Accepted to appear in the Journal of Graph Theor
- …