7,090 research outputs found

    Improving the Asymmetric TSP by Considering Graph Structure

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    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

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    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

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    In a directed graph GG 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 (2+Δ,O(n0.5+Δ))(2+\varepsilon,O(n^{0.5+\varepsilon}))-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~2+Δ2+\varepsilon. 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 (1+Δ,O(∣R∣Δ))(1+\varepsilon,O(|R|^{\varepsilon}))-ap\-proxi\-ma\-tion, where RR are the terminals. Finally, we show how to apply our results to obtain an (α+Δ,O(n0.5+Δ))(\alpha+\varepsilon,O(n^{0.5+\varepsilon}))-approximation for \emph{light-weight directed α\alpha-spanners}. For this, no non-trivial approximation algorithm has been known before. All running times depends on nn and Δ\varepsilon and are polynomial in nn for any fixed Δ>0\varepsilon>0

    On morphological hierarchical representations for image processing and spatial data clustering

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    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

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    Given a directed graph GG with non negative cost on the arcs, a directed tree cover of GG is a rooted directed tree such that either head or tail (or both of them) of every arc in GG is touched by TT. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be NPNP-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 max⁥{2,ln⁥(D+)}\max\{2, \ln(D^+)\} with D+D^+ is the maximum outgoing degree of the nodes in GG.Comment: 13 page

    Computational Complexity for Physicists

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    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

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    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

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    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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