Abstract: A method and apparatus for using tag topology for enhancing search capabilities, e.g., searching over the web, are disclosed. For example, the present method receives a user query contain a search term from a user. The method then generates a search result containing at least one entity, wherein the at least one entity is found based on a plurality of user provided tags that is associated with the at least one entity.

Abstract: A method and apparatus for using tag topology for enhancing search capabilities, e.g., searching over the web, are disclosed. For example, the present method receives a user query contain a search term from a user. The method then generates a search result containing at least one entity, wherein the at least one entity is found based on a plurality of user provided tags that is associated with the at least one entity.

Abstract: A method for registering multiple 3D point sets by determining optimal relative positions and orientations of the 3D point sets. Initial values are determined for the rotation matrices corresponding to the relative orientations of reference frames of the 3D point sets. A registration error cost function is optimized on a product manifold of all of the rotation matrices to determine optimal values of the rotation matrices. The optimal values of the rotation matrices are used to determine optimal values for translation vectors corresponding to the relative positions of the reference frames of the 3D point sets. The 3D point sets are registered on a common reference frame using the optimal rotation matrices and the optimal translation vectors.

Abstract: A method and apparatus for using tag topology for enhancing search capabilities, e.g., searching over the web, are disclosed. For example, the present method receives a user query contain a search term from a user. The method then generates a search result containing at least one entity, wherein the at least one entity is found based on a plurality of user provided tags that is associated with the at least one entity.

Abstract: A method and apparatus for using tag topology for enhancing search capabilities, e.g., searching over the web, are disclosed. For example, the present method receives a user query contain a search term from a user. The method then generates a search result containing at least one entity, wherein the at least one entity is found based on a plurality of user provided tags that is associated with the at least one entity.

Abstract: A method and apparatus for using tag topology for enhancing search capabilities, e.g., searching over the web, are disclosed. For example, the present method receives a user query contain a search term from a user. The method then generates a search result containing at least one entity, wherein the at least one entity is found based on a plurality of user provided tags that is associated with the at least one entity.

Abstract: A method and apparatus for rapid identification of column heterogeneity in databases are disclosed. For example, the method receives data associated with a column in a database. The method computes a cluster entropy for the data as a measure of data heterogeneity and then determines whether said data is heterogeneous in accordance with the cluster entropy.

Abstract: A method for registering multiple 3D point sets by determining optimal relative positions and orientations of the 3D point sets. Initial values are determined for the rotation matrices corresponding to the relative orientations of reference frames of the 3D point sets. A registration error cost function is optimized on a product manifold of all of the rotation matrices to determine optimal values of the rotation matrices. The optimal values of the rotation matrices are used to determine optimal values for translation vectors corresponding to the relative positions of the reference frames of the 3D point sets. The 3D point sets are registered on a common reference frame using the optimal rotation matrices and the optimal translation vectors.

Abstract: A method for registering multiple 3D point sets by determining optimal relative positions and orientations of the 3D point sets. Initial values are determined for the rotation matrices corresponding to the relative orientations of reference frames of the 3D point sets. A registration error cost function is optimized on a product manifold of all of the rotation matrices to determine optimal values of the rotation matrices. The optimal values of the rotation matrices are used to determine optimal values for translation vectors corresponding to the relative positions of the reference frames of the 3D point sets. The 3D point sets are registered on a common reference frame using the optimal rotation matrices and the optimal translation vectors.

Abstract: A method and apparatus for using tag topology for enhancing search capabilities, e.g., searching over the web, are disclosed. For example, the present method receives a user query contain a search term from a user. The method then generates a search result containing at least one entity, wherein the at least one entity is found based on a plurality of user provided tags that is associated with the at least one entity.

Abstract: A map simplification system performs dynamic view dependent simplification of relatively large geographic maps.

Abstract: A server computer is provided for representing and navigating the connectivity of Web pages. The Web pages include links to other Web pages. The links and Web page s have associated names (URLs). The names of the Web pages are sorted in a memory of the connectivity server. The sorted names are delta encoded while periodically storing full names as checkpoints in the memory. Each delta encoded name and checkpoint has a unique identification. A list of pairs of identifications representing existent links is sorted twice, first according to the first identification of each pair to produce an inlist, and second according to the second identification of each pair to produce an outlist. An array of elements is stored in the memory, there is one array element for each Web page. Each element includes a first pointer to one of the checkpoints, a second pointer to an associated inlist of the Web page, and a third pointer to an associated outlist of the Web page.