7,090 research outputs found
Improving the Asymmetric TSP by Considering Graph Structure
Recent works on cost based relaxations have improved Constraint Programming
(CP) models for the Traveling Salesman Problem (TSP). We provide a short survey
over solving asymmetric TSP with CP. Then, we suggest new implied propagators
based on general graph properties. We experimentally show that such implied
propagators bring robustness to pathological instances and highlight the fact
that graph structure can significantly improve search heuristics behavior.
Finally, we show that our approach outperforms current state of the art
results.Comment: Technical repor
New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones
We study three representations of hierarchies of partitions: dendrograms
(direct representations), saliency maps, and minimum spanning trees. We provide
a new bijection between saliency maps and hierarchies based on quasi-flat zones
as used in image processing and characterize saliency maps and minimum spanning
trees as solutions to constrained minimization problems where the constraint is
quasi-flat zones preservation. In practice, these results form a toolkit for
new hierarchical methods where one can choose the most convenient
representation. They also invite us to process non-image data with
morphological hierarchies
Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees
In a directed graph with non-correlated edge lengths and costs, the
\emph{network design problem with bounded distances} asks for a cost-minimal
spanning subgraph subject to a length bound for all node pairs. We give a
bi-criteria -approximation for this
problem. This improves on the currently best known linear approximation bound,
at the cost of violating the distance bound by a factor of at
most~.
In the course of proving this result, the related problem of \emph{directed
shallow-light Steiner trees} arises as a subproblem. In the context of directed
graphs, approximations to this problem have been elusive. We present the first
non-trivial result by proposing a
-ap\-proxi\-ma\-tion, where are the
terminals.
Finally, we show how to apply our results to obtain an
-approximation for
\emph{light-weight directed -spanners}. For this, no non-trivial
approximation algorithm has been known before. All running times depends on
and and are polynomial in for any fixed
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
Approximating the minimum directed tree cover
Given a directed graph with non negative cost on the arcs, a directed
tree cover of is a rooted directed tree such that either head or tail (or
both of them) of every arc in is touched by . The minimum directed tree
cover problem (DTCP) is to find a directed tree cover of minimum cost. The
problem is known to be -hard. In this paper, we show that the weighted Set
Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to
approximate DTCP with the same ratio as for SCP. We show that this expectation
can be satisfied in some way by designing a purely combinatorial approximation
algorithm for the DTCP and proving that the approximation ratio of the
algorithm is with is the maximum outgoing degree of
the nodes in .Comment: 13 page
Computational Complexity for Physicists
These lecture notes are an informal introduction to the theory of
computational complexity and its links to quantum computing and statistical
mechanics.Comment: references updated, reprint available from
http://itp.nat.uni-magdeburg.de/~mertens/papers/complexity.shtm
On Computing the Translations Norm in the Epipolar Graph
This paper deals with the problem of recovering the unknown norm of relative
translations between cameras based on the knowledge of relative rotations and
translation directions. We provide theoretical conditions for the solvability
of such a problem, and we propose a two-stage method to solve it. First, a
cycle basis for the epipolar graph is computed, then all the scaling factors
are recovered simultaneously by solving a homogeneous linear system. We
demonstrate the accuracy of our solution by means of synthetic and real
experiments.Comment: Accepted at 3DV 201
A network dynamics approach to chemical reaction networks
A crisp survey is given of chemical reaction networks from the perspective of
general nonlinear network dynamics, in particular of consensus dynamics. It is
shown how by starting from the complex-balanced assumption the reaction
dynamics governed by mass action kinetics can be rewritten into a form which
allows for a very simple derivation of a number of key results in chemical
reaction network theory, and which directly relates to the thermodynamics of
the system. Central in this formulation is the definition of a balanced
Laplacian matrix on the graph of chemical complexes together with a resulting
fundamental inequality. This directly leads to the characterization of the set
of equilibria and their stability. Both the form of the dynamics and the
deduced dynamical behavior are very similar to consensus dynamics. The
assumption of complex-balancedness is revisited from the point of view of
Kirchhoff's Matrix Tree theorem, providing a new perspective. Finally, using
the classical idea of extending the graph of chemical complexes by an extra
'zero' complex, a complete steady-state stability analysis of mass action
kinetics reaction networks with constant inflows and mass action outflows is
given.Comment: 18 page
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