7,810 research outputs found
Dynamic Programming on Nominal Graphs
Many optimization problems can be naturally represented as (hyper) graphs,
where vertices correspond to variables and edges to tasks, whose cost depends
on the values of the adjacent variables. Capitalizing on the structure of the
graph, suitable dynamic programming strategies can select certain orders of
evaluation of the variables which guarantee to reach both an optimal solution
and a minimal size of the tables computed in the optimization process. In this
paper we introduce a simple algebraic specification with parallel composition
and restriction whose terms up to structural axioms are the graphs mentioned
above. In addition, free (unrestricted) vertices are labelled with variables,
and the specification includes operations of name permutation with finite
support. We show a correspondence between the well-known tree decompositions of
graphs and our terms. If an axiom of scope extension is dropped, several
(hierarchical) terms actually correspond to the same graph. A suitable
graphical structure can be found, corresponding to every hierarchical term.
Evaluating such a graphical structure in some target algebra yields a dynamic
programming strategy. If the target algebra satisfies the scope extension
axiom, then the result does not depend on the particular structure, but only on
the original graph. We apply our approach to the parking optimization problem
developed in the ASCENS e-mobility case study, in collaboration with
Volkswagen. Dynamic programming evaluations are particularly interesting for
autonomic systems, where actual behavior often consists of propagating local
knowledge to obtain global knowledge and getting it back for local decisions.Comment: In Proceedings GaM 2015, arXiv:1504.0244
Congruence Testing of Point Sets in 4-Space
We give a deterministic O(n log n)-time algorithm to decide if two n-point sets in 4-dimensional Euclidean space are the same up to rotations and translations. It has been conjectured that O(n log n) algorithms should exist for any fixed dimension. The best algorithms in d-space so far are a deterministic algorithm by Brass and Knauer [Int. J. Comput. Geom. Appl., 2000] and a randomized Monte Carlo algorithm by Akutsu [Comp. Geom., 1998]. They take time O(n^2 log n) and O(n^(3/2) log n) respectively in 4-space. Our algorithm exploits many geometric structures and properties of 4-dimensional space
Identifying residential sub-markets using intra-urban migrations: the case of study of Barcelona’s neighborhoods
The dynamic evolution of the real estate market, as well as the sophistications of the interactions of
the actors involved in it have caused that, contrary to classical economic theory, the real estate market is increasingly being thought of as a set of submarkets. This is because, among other things, the
modeling of a segmented housing market allows, on the one hand, to design housing policies that are better adapted to the needs of the population, but on the other hand, it allows the generation of both
marketing and supply strategies Oriented to specific population sectors. Such strategies in theory should behave as options with relatively low uncertainty, thus representing an attractive offer to all
market players. However, in praxis, the segmentation of the real estate market is usually modeled on the offer. It is therefore that this paper proposes a modeling from observed preferences3 seen through
intraurban migrations. In particular, it is proposed to model the market through the interaction value of Coombes, scaling the results in order to visualize the resulting submarket structure from the
construction of a PAM (Partitioning Algorithm Medoids).Peer ReviewedPostprint (published version
Stable Camera Motion Estimation Using Convex Programming
We study the inverse problem of estimating n locations (up to
global scale, translation and negation) in from noisy measurements of a
subset of the (unsigned) pairwise lines that connect them, that is, from noisy
measurements of for some pairs (i,j) (where the
signs are unknown). This problem is at the core of the structure from motion
(SfM) problem in computer vision, where the 's represent camera locations
in . The noiseless version of the problem, with exact line measurements,
has been considered previously under the general title of parallel rigidity
theory, mainly in order to characterize the conditions for unique realization
of locations. For noisy pairwise line measurements, current methods tend to
produce spurious solutions that are clustered around a few locations. This
sensitivity of the location estimates is a well-known problem in SfM,
especially for large, irregular collections of images.
In this paper we introduce a semidefinite programming (SDP) formulation,
specially tailored to overcome the clustering phenomenon. We further identify
the implications of parallel rigidity theory for the location estimation
problem to be well-posed, and prove exact (in the noiseless case) and stable
location recovery results. We also formulate an alternating direction method to
solve the resulting semidefinite program, and provide a distributed version of
our formulation for large numbers of locations. Specifically for the camera
location estimation problem, we formulate a pairwise line estimation method
based on robust camera orientation and subspace estimation. Lastly, we
demonstrate the utility of our algorithm through experiments on real images.Comment: 40 pages, 12 figures, 6 tables; notation and some unclear parts
updated, some typos correcte
A Geometric Approach to the Problem of Unique Decomposition of Processes
This paper proposes a geometric solution to the problem of prime
decomposability of concurrent processes first explored by R. Milner and F.
Moller in [MM93]. Concurrent programs are given a geometric semantics using
cubical areas, for which a unique factorization theorem is proved. An effective
factorization method which is correct and complete with respect to the
geometric semantics is derived from the factorization theorem. This algorithm
is implemented in the static analyzer ALCOOL.Comment: 15 page
Computational Aspects of the Hausdorff Distance in Unbounded Dimension
We study the computational complexity of determining the Hausdorff distance
of two polytopes given in halfspace- or vertex-presentation in arbitrary
dimension. Subsequently, a matching problem is investigated where a convex body
is allowed to be homothetically transformed in order to minimize its Hausdorff
distance to another one. For this problem, we characterize optimal solutions,
deduce a Helly-type theorem and give polynomial time (approximation) algorithms
for polytopes
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