We introduce the Fast Marching farthest point sampling (FastFPS) approach for the progressive sampling of planar domains and curved manifolds in triangulated, point cloud or implicit form. By using Fast Marching methods2, 3, 6 for the incremental computation of distance maps across the sampling domain, we obtain a farthest point sampling technique superior to earlier point sampling principles i...

The farthest string problem (FARTHEST STRING) is one of the core problems in the field of consensus word analysis and several biological problems such as discovering potential drugs, universal primers, or unbiased consensus sequences. Given k strings of the same length L and a nonnegative integer d, FARTHEST STRING is to find a string s such that none of the given strings has a Hamming distance...

We present an indexing scheme that is capable of answering a broad range of complex top-k queries that contain a scalar product between two vectors when one of the vectors is present in the database, while the other one arrives at query time. Specifically we provide indexing facilities for the top-k closest points below (above) a hyperplane and the top-k farthest points below (above) a hyperpla...

Let P be a set of n points in the plane. The k-nearest neighbor (k-NN) query problem is to preprocess P into a data structure that quickly reports k closest points in P for a query point q. This paper addresses a generalization of the k-NN query problem to a query set Q of points, namely, the group nearest neighbor problem, in the L1 plane. More precisely, a query is assigned with a set Q of at...