With the proliferation of location-based services, geo-textual data is becoming ubiquitous. Objects involved in include geospatial locations, textual descriptions or keywords, and various attributes (e.g., a point-of-interest has its expenses users' ratings). One prominent type spatial keyword queries to find, for query consisting location set objects that covers all keywords good quality accor...

Proof: (by induction). We want to show that one SAP doesn’t introduce negative cycles in Gf . Initially there are no negative cost cycles. Feasible prices can be computed by using shortest path distances from s. After finding the shortest s-t path, it has reduced cost 0. Every arc on the path has reduced length 0. This demonstrates that the triangle inequality property is tight on shortest path...

Di erent phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [16] or from di erent genes [12] in the study of molecular evolution. Comparing these trees to nd their similarities and dissimilarities (i.e. distance) is thus an important issue in computational molecular biology. Several distance metrics including the nearest...

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

multiple traveling salesman problem (mtsp) is one of the most popular operation research problem and is known as combinatorial optimization problems. mtsp is an extension version of the famous and widely used problem named traveling salesman problem (tsp). because of its benefices in various domains, many researchers have tried to solve that, and many methods have proposed so far. mtsp is a np-...

During the last decade Optimal Transport had a relevant role in study of geometry singular spaces that culminated with Lott–Sturm–Villani theory. The latter is built on characterisation Ricci curvature lower bounds terms displacement convexity certain entropy functionals along W 2 -geodesics. Substantial recent advancements theory (localization paradigm and local-to-global property) have been o...