Results 1  10
of
15
Aggregate Nearest Neighbor Queries in Spatial Databases
 TODS
, 2005
"... Given two spatial datasets P (e.g., facilities) and Q (queries), an aggregate nearest neighbor (ANN) query retrieves the point(s) of P with the smallest aggregate distance(s) to points in Q. Assuming, for example, n users at locations q1,... qn,anANN query outputs the facility p ∈ P that minimizes t ..."
Abstract

Cited by 59 (6 self)
 Add to MetaCart
Given two spatial datasets P (e.g., facilities) and Q (queries), an aggregate nearest neighbor (ANN) query retrieves the point(s) of P with the smallest aggregate distance(s) to points in Q. Assuming, for example, n users at locations q1,... qn,anANN query outputs the facility p ∈ P that minimizes the sum of distances pqi  for 1 ≤ i ≤ n that the users have to travel in order to meet there. Similarly, another ANN query may report the point p ∈ P that minimizes the maximum distance that any user has to travel, or the minimum distance from some user to his/her closest facility. If Q fits in memory and P is indexed by an Rtree, we develop algorithms for aggregate nearest neighbors that capture several versions of the problem, including weighted queries and incremental reporting of results. Then, we analyze their performance and propose cost models for query optimization. Finally, we extend our techniques for diskresident queries and approximate ANN retrieval. The efficiency of the algorithms and the accuracy of the cost models are evaluated through extensive experiments with real and synthetic datasets.
Close Pair Queries in Moving Object Databases
 GIS'05
, 2005
"... Databases of moving objects are important for air traffic control, ground traffic, and battlefield configurations. We introduce the (historical and spatial) range closepair query for moving objects as an important problem for such databases. The purpose of a range closepair query for moving object ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Databases of moving objects are important for air traffic control, ground traffic, and battlefield configurations. We introduce the (historical and spatial) range closepair query for moving objects as an important problem for such databases. The purpose of a range closepair query for moving objects is to find pairs of objects that were closer than ɛ during time interval I and within spatial range R, where ɛ, I and R are userspecified parameters. This paper solves the range closepair query using two components: the retrieval component and the closepair identification component. The retrieval component breaks up long trajectories into trajectory segments, which are produced in increasing time order, without the need for sorting. The retrieval component takes advantage of a new index mechanism, the Multiple TSBtree. The segments are then pipelined to the closepair identification component. The identification component introduces a novel spatial sweep that sweeps by time and one spatial dimension at the same time. Extensive experimental results are provided, demonstrating the advantages of the new approach when considering close pairs.
A Unified Approach for Computing Topk Pairs in Multidimensional Space
"... Abstract—Topk pairs queries have many real applications. k closest pairs queries, k furthest pairs queries and their bichromatic variants are some of the examples of the topk pairs queries that rank the pairs on distance functions. While these queries have received significant research attention, ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
(Show Context)
Abstract—Topk pairs queries have many real applications. k closest pairs queries, k furthest pairs queries and their bichromatic variants are some of the examples of the topk pairs queries that rank the pairs on distance functions. While these queries have received significant research attention, there does not exist a unified approach that can efficiently answer all these queries. Moreover, there is no existing work that supports topk pairs queries based on generic scoring functions. In this paper, we present a unified approach that supports a broad class of topk pairs queries including the queries mentioned above. Our proposed approach allows the users to define a local scoring function for each attribute involved in the query and a global scoring function that computes the final score of each pair by combining its scores on different attributes. We propose efficient internal and external memory algorithms and our theoretical analysis shows that the expected performance of the algorithms is optimal when two or less attributes are involved. Our approach does not require any prebuilt indexes, is easy to implement and has low memory requirement. We conduct extensive experiments to demonstrate the efficiency of our proposed approach. I.
On the power of the semiseparated pair decomposition
 WADS, LNCS Volume
"... s> 1, of a set S ⊂ R d is a set {(Ai, Bi)} of pairs of subsets of S such that for each i, there are balls DA i and DB i containing Ai and Bi respectively such that d(DA i, DB i) ≥ s · min(radius(DA i), radius(DB i and for any two points p, q ∈ S there is a unique index i such that p ∈ Ai and q ∈ ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
s> 1, of a set S ⊂ R d is a set {(Ai, Bi)} of pairs of subsets of S such that for each i, there are balls DA i and DB i containing Ai and Bi respectively such that d(DA i, DB i) ≥ s · min(radius(DA i), radius(DB i and for any two points p, q ∈ S there is a unique index i such that p ∈ Ai and q ∈ Bi or viceversa. In this paper, we use the SSPD to obtain the following results: First, we consider the construction of geometric tspanners in the context of imprecise points and we prove that any set S ⊂ R d of n imprecise points, modeled as pairwise disjoint balls, admits a tspanner with O(n log n/(t − 1) d) edges which can be computed in O(n log n/(t − 1) d) time. If all balls have the same radius, the number of edges reduces to O(n/(t − 1) d). Secondly, for a set of n points in the plane, we design a query data structure for halfplane closestpair queries that can be built in O(n 2 log 2 n) time using O(n log n) space and answers a query in O(n 1/2+ε) time, for any ε> 0. By reducing the preprocessing time to O(n 1+ε) and using O(n log 2 n) space, the query can be answered in O(n 3/4+ε) time. Moreover, we improve the preprocessing time of an existing axisparallel rectangle closestpair query data structure from quadratic to nearlinear. Finally, we revisit some previously studied problems, namely spanners for complete kpartite graphs and lowdiameter spanners, and show how to use the SSPD to obtain simple algorithms for these problems. 1
Data structures for rangeaggregate extent queries
 In Proc. 20th CCCG
, 2008
"... A fundamental and wellstudied problem in computational geometry is range searching, where the goal is to preprocess a set, S, of geometric objects (e.g., points in the plane) so that the subset S ′ ⊆ S that is contained in a query range (e.g., an axesparallel rectangle) can be reported efficientl ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
A fundamental and wellstudied problem in computational geometry is range searching, where the goal is to preprocess a set, S, of geometric objects (e.g., points in the plane) so that the subset S ′ ⊆ S that is contained in a query range (e.g., an axesparallel rectangle) can be reported efficiently. However, in many situations, what is of interest is to generate a more informative “summary ” of the output, obtained by applying a suitable aggregation function on S ′. Examples of such aggregation functions include count, sum, min, max, mean, median, mode, and topk that are usually computed on a set of weights defined suitably on the objects. Such rangeaggregate query problems have been the subject of much recent research in both the database and the computational geometry communities. In this paper, we further generalize this line of work by considering aggregation functions on pointsets that measure the extent or “spread ” of the objects in the retrieved set S ′. The functions considered here include closest pair, diameter, and width. The challenge here is that these aggregation functions (unlike, say, count) are not efficiently decomposable in the sense that the answer to S ′ cannot be inferred easily from answers to subsets that induce a partition
Efficiently Monitoring Topk Pairs over Sliding Windows
"... Abstract—Topk pairs queries have received significant attention by the research community. kclosest pairs queries, kfurthest pairs queries and their variants are among the most well studied special cases of the topk pairs queries. In this paper, we present the first approach to answer a broad cl ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
Abstract—Topk pairs queries have received significant attention by the research community. kclosest pairs queries, kfurthest pairs queries and their variants are among the most well studied special cases of the topk pairs queries. In this paper, we present the first approach to answer a broad class of topk pairs queries over sliding windows. Our framework handles multiple topk pairs queries and each query is allowed to use a different scoring function, a different value of k and a different size of the sliding window. Although the number of possible pairs in the sliding window is quadratic to the number of objects N in the sliding window, we efficiently answer the topk pairs query by maintaining a small subset of pairs called Kskyband which is expected to consist of O(K log(N/K)) pairs. For all the queries that use the same scoring function, we need to maintain only oneKskyband. We present efficient techniques for the Kskyband maintenance and query answering. We conduct a detailed complexity analysis and show that the expected cost of our approach is reasonably close to the lower bound cost. We experimentally verify this by comparing our approach with a specially designed supreme algorithm that assumes the existence of an oracle and meets the lower bound cost. I.
RangeAggregate Proximity Queries
"... In a rangeaggegate query problem we wish to preprocess a set S of geometric objects such that given a query orthogonal range q, a certain intersection or proximity query on the objects of S intersected by q can be answered efficiently. Although rangeaggregate queries have been widely investigated ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
In a rangeaggegate query problem we wish to preprocess a set S of geometric objects such that given a query orthogonal range q, a certain intersection or proximity query on the objects of S intersected by q can be answered efficiently. Although rangeaggregate queries have been widely investigated in the past for aggregation functions like average, count, min, max, sum etc. there is little work on proximity problems. In this paper, we solve two problems. We first consider the problem of determining if any pair of points in a query orthogonal rectangle are within a constant λ of each other and give a solution that takes O(n log 2+ɛ n) space and O(log 2 n) query time. Subsequently, we solve the problem of finding the closest pair in a query orthogonal rectangle which takes O(n log 3 n) space and O(log 3 n) query time.
Continuous Spatiotemporal Trajectory Joins
"... Abstract. Given the plethora of GPS and locationbased services, que ries over trajectories have recently received much attention. In this paper we examine trajectory joins over streaming spatiotemporal data. Given a stream of spatiotemporal trajectories created by monitored moving objects, the out ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Given the plethora of GPS and locationbased services, que ries over trajectories have recently received much attention. In this paper we examine trajectory joins over streaming spatiotemporal data. Given a stream of spatiotemporal trajectories created by monitored moving objects, the outcome of a Continuous Spatiotemporal Trajectory Join (CSTJ) query is the set of objects in the stream, which have shown similar behavior over a queryspecified time interval, relative to the current timestamp. We propose a novel indexing scheme for streaming spatiotemporal data and develop algorithms for CSTJ evaluation, which utilize the proposed indexing scheme and effectively reduce the computation cost and I/O operations. Finally, we present a thorough experimental evaluation of the proposed indexing structure and algorithms. 1
Processing distance join queries with constraints
 The Computer Journal
, 2006
"... Distancejoin queries are used in many modern applications, such as spatial databases, spatiotemporal databases, and data mining. One of the most common distancejoin queries is the closestpair query. Given two datasets DA and DB the closestpair query (CPQ) retrieves the pair (a,b), where a ∈ DA a ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Distancejoin queries are used in many modern applications, such as spatial databases, spatiotemporal databases, and data mining. One of the most common distancejoin queries is the closestpair query. Given two datasets DA and DB the closestpair query (CPQ) retrieves the pair (a,b), where a ∈ DA and b ∈ DB, having the smallest distance between all pairs of objects. An extension to this problem is to generate the k closest pairs of objects (kCPQ). In several cases spatial constraints are applied, and object pairs that are retrieved must also satisfy these constraints. Although the application of spatial constraints seems natural towards a more focused search, only recently they have been studied for the CPQ problem with the restriction that DA = DB. In this work, we focus on constrained closestpair queries (CCPQ), between two distinct datasets DA and DB, where objects from DA must be enclosed by a spatial region R. Several algorithms are presented and evaluated using reallife and synthetic datasets. Among them, a heapbased method enhanced with batch capabilities outperforms the other approaches as it is demonstrated by an extensive performance evaluation.
Closest Pair Queries with Spatial Constraints ⋆
"... Abstract. Given two datasets DA and DB the closestpair query (CPQ) retrieves the pair (a,b), where a ∈ DA and b ∈ DB, having the smallest distance between all pairs of objects. An extension to this problem is to generate the k closest pairs of objects (kCPQ). In several cases spatial constraints a ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Given two datasets DA and DB the closestpair query (CPQ) retrieves the pair (a,b), where a ∈ DA and b ∈ DB, having the smallest distance between all pairs of objects. An extension to this problem is to generate the k closest pairs of objects (kCPQ). In several cases spatial constraints are applied, and object pairs that are retrieved must also satisfy these constraints. Although the application of spatial constraints seems natural towards a more focused search, only recently they have been studied for the CPQ problem with the restriction that DA = DB. In this work we focus on constrained closestpair queries (CCPQ), between two distinct datasets DA and DB, where objects from DA must be enclosed by a spatial region R. A new algorithm is proposed, which is compared with a modified closestpair algorithm. The experimental results demonstrate that the proposed approach is superior with respect to CPU and I/O costs. 1