In this paper, we present algorithms for the top-k nearest neighbor searching where the input points are exact and the query point is uncertain under the L1 metric in the plane. The uncertain query point is represented by a discrete probability distribution function, and the goal is to efficiently return the top-k expected nearest neighbors, which have the smallest expected distances to the que...

The classical k nearest neighbor (k-nn) classification assumes that a fixed global metric is defined and searching for nearest neighbors is always based on this global metric. In the paper we present a model with local induction of a metric. Any test object induces a local metric from the neighborhood of this object and selects k nearest neighbors according to this locally induced metric. To in...

We prove that the spaces of unrooted phylogenetic trees are Hamiltonian for two popular search metrics: Subtree Prune and Regraft (SPR) and Tree Bisection and Reconnection (TBR). Further, we make progress on two conjectures of Bryant on searching phylogenetic treespace: treespace under the Nearest Neighbor Interchange (NNI) metric has a 2-walk, and there exists SPR neighborhoods without complet...

Over the last decade, an immense amount of data has become available. From collections of photos, to genetic data, and to network traffic statistics, modern technologies and cheap storage have made it possible to accumulate huge datasets. But how can we effectively use all this data? The ever growing sizes of the datasets make it imperative to design new algorithms capable of sifting through th...

For nearest neighbor search, a user queries a server for nearby points of interest (POIs) with his/her location information. Our aim is to protect the user’s sensitive information against adversaries including the location-based service itself. Most research efforts have elaborated on reasonable trade-offs between privacy and utility. We propose a framework based on range search query without a...

Many classic data structures have been proposed to support geometric queries, such as range search, point location and nearest neighbor search. For a two-dimensional geometric data set consisting of n elements, these structures typically require O(n), close to O(n) or O(n lg n) words of space; while they support efficient queries, their storage costs are often much larger than the space require...

Collection of appropriate qualitative and quantitative data is necessary for proper management and planning. Used the suitable inventory methods is necessary and accuracy of sampling methods dependent the inventory net and number of sample point. Nearest neighbor sampling method is a one of distance methods and calculated by three equations (Byth and Riple, 1980; Cotam and Curtis, 1956 and Cota...

Uncertain data are abundant in numerous spatiotemporal applications providing location-based services. This chapter will first review these applications and explain why uncertainty is inherent, sometimes even intended, in their underlying data. Then, we will address two classical spatial queries: range search and nearest neighbor retrieval. We will see that the presence of uncertainty requires ...