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Computing the GromovHausdorff Distance for Metric Trees∗
"... The GromovHausdorff distance is a natural way to measure distance between two metric spaces. We give the first proof of hardness and first nontrivial approximation algorithm for computing the GromovHausdorff distance for geodesic metrics in trees. Specifically, we prove it is NPhard to approxima ..."
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The GromovHausdorff distance is a natural way to measure distance between two metric spaces. We give the first proof of hardness and first nontrivial approximation algorithm for computing the GromovHausdorff distance for geodesic metrics in trees. Specifically, we prove it is NP
Gromovhausdorff distances in Euclidean spaces
 In Proc. Computer Vision and Pattern Recognition (CVPR
"... The purpose of this paper is to study the relationship between measures of dissimilarity between shapes in Euclidean space. We first concentrate on the pair GromovHausdorff distance (GH) versus Hausdorff distance under the action of Euclidean isometries (EH). Then, we (1) show they are comparable i ..."
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Cited by 18 (6 self)
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The purpose of this paper is to study the relationship between measures of dissimilarity between shapes in Euclidean space. We first concentrate on the pair GromovHausdorff distance (GH) versus Hausdorff distance under the action of Euclidean isometries (EH). Then, we (1) show they are comparable
Matricial quantum GromovHausdorff distance
 J. Funct. Anal
"... Abstract. We develop a matricial version of Rieffel’s GromovHausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C ∗algebras. Our approach yields a metric space of “isometric ” unital complete order isomorphism classes of metrized operator systems ..."
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Cited by 26 (1 self)
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Abstract. We develop a matricial version of Rieffel’s GromovHausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C ∗algebras. Our approach yields a metric space of “isometric ” unital complete order isomorphism classes of metrized operator systems
GROMOVHAUSDORFF ULTRAMETRIC
, 2005
"... Abstract. We show that there exists a natural counterpart of the GromovHausdorff metric in the class of ultrametric spaces. It is proved, in particular, that the space of all ultrametric spaces whose metric take values in a fixed countable set is homeomorphic to the space of irrationals. 1. ..."
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Abstract. We show that there exists a natural counterpart of the GromovHausdorff metric in the class of ultrametric spaces. It is proved, in particular, that the space of all ultrametric spaces whose metric take values in a fixed countable set is homeomorphic to the space of irrationals. 1.
GromovHausdorff distance for quantum metric spaces
 Mem. Amer. Math. Soc
"... Abstract. By a quantum metric space we mean a C ∗algebra (or more generally an orderunit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov–Hausdorff distanc ..."
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Cited by 57 (7 self)
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Abstract. By a quantum metric space we mean a C ∗algebra (or more generally an orderunit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov–Hausdorff
Vector bundles and GromovHausdorff distance
, 2007
"... We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov– Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projectionvalued functio ..."
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Cited by 14 (4 self)
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We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov– Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection
Results 1  10
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