98,363 research outputs found
A Static Optimality Transformation with Applications to Planar Point Location
Over the last decade, there have been several data structures that, given a
planar subdivision and a probability distribution over the plane, provide a way
for answering point location queries that is fine-tuned for the distribution.
All these methods suffer from the requirement that the query distribution must
be known in advance.
We present a new data structure for point location queries in planar
triangulations. Our structure is asymptotically as fast as the optimal
structures, but it requires no prior information about the queries. This is a
2D analogue of the jump from Knuth's optimum binary search trees (discovered in
1971) to the splay trees of Sleator and Tarjan in 1985. While the former need
to know the query distribution, the latter are statically optimal. This means
that we can adapt to the query sequence and achieve the same asymptotic
performance as an optimum static structure, without needing any additional
information.Comment: 13 pages, 1 figure, a preliminary version appeared at SoCG 201
The Flexible Group Spatial Keyword Query
We present a new class of service for location based social networks, called
the Flexible Group Spatial Keyword Query, which enables a group of users to
collectively find a point of interest (POI) that optimizes an aggregate cost
function combining both spatial distances and keyword similarities. In
addition, our query service allows users to consider the tradeoffs between
obtaining a sub-optimal solution for the entire group and obtaining an
optimimized solution but only for a subgroup.
We propose algorithms to process three variants of the query: (i) the group
nearest neighbor with keywords query, which finds a POI that optimizes the
aggregate cost function for the whole group of size n, (ii) the subgroup
nearest neighbor with keywords query, which finds the optimal subgroup and a
POI that optimizes the aggregate cost function for a given subgroup size m (m
<= n), and (iii) the multiple subgroup nearest neighbor with keywords query,
which finds optimal subgroups and corresponding POIs for each of the subgroup
sizes in the range [m, n]. We design query processing algorithms based on
branch-and-bound and best-first paradigms. Finally, we provide theoretical
bounds and conduct extensive experiments with two real datasets which verify
the effectiveness and efficiency of the proposed algorithms.Comment: 12 page
Reverse k Nearest Neighbor Search over Trajectories
GPS enables mobile devices to continuously provide new opportunities to
improve our daily lives. For example, the data collected in applications
created by Uber or Public Transport Authorities can be used to plan
transportation routes, estimate capacities, and proactively identify low
coverage areas. In this paper, we study a new kind of query-Reverse k Nearest
Neighbor Search over Trajectories (RkNNT), which can be used for route planning
and capacity estimation. Given a set of existing routes DR, a set of passenger
transitions DT, and a query route Q, a RkNNT query returns all transitions that
take Q as one of its k nearest travel routes. To solve the problem, we first
develop an index to handle dynamic trajectory updates, so that the most
up-to-date transition data are available for answering a RkNNT query. Then we
introduce a filter refinement framework for processing RkNNT queries using the
proposed indexes. Next, we show how to use RkNNT to solve the optimal route
planning problem MaxRkNNT (MinRkNNT), which is to search for the optimal route
from a start location to an end location that could attract the maximum (or
minimum) number of passengers based on a pre-defined travel distance threshold.
Experiments on real datasets demonstrate the efficiency and scalability of our
approaches. To the best of our best knowledge, this is the first work to study
the RkNNT problem for route planning.Comment: 12 page
Orthogonal Point Location and Rectangle Stabbing Queries in 3-d
In this work, we present a collection of new results on two fundamental problems in geometric data structures: orthogonal point location and rectangle stabbing.
- Orthogonal point location. We give the first linear-space data structure that supports 3-d point location queries on n disjoint axis-aligned boxes with optimal O(log n) query time in the (arithmetic) pointer machine model. This improves the previous O(log^{3/2} n) bound of Rahul [SODA 2015]. We similarly obtain the first linear-space data structure in the I/O model with optimal query cost, and also the first linear-space data structure in the word RAM model with sub-logarithmic query time.
- Rectangle stabbing. We give the first linear-space data structure that supports 3-d 4-sided and 5-sided rectangle stabbing queries in optimal O(log_wn+k) time in the word RAM model. We similarly obtain the first optimal data structure for the closely related problem of 2-d top-k rectangle stabbing in the word RAM model, and also improved results for 3-d 6-sided rectangle stabbing.
For point location, our solution is simpler than previous methods, and is based on an interesting variant of the van Emde Boas recursion, applied in a round-robin fashion over the dimensions, combined with bit-packing techniques. For rectangle stabbing, our solution is a variant of Alstrup, Brodal, and Rauhe\u27s grid-based recursive technique (FOCS 2000), combined with a number of new ideas
Cleaning uncertain data for top-k queries
The information managed in emerging applications, such as sensor networks, location-based services, and data integration, is inherently imprecise. To handle data uncertainty, probabilistic databases have been recently developed. In this paper, we study how to quantify the ambiguity of answers returned by a probabilistic top-k query. We develop efficient algorithms to compute the quality of this query under the possible world semantics. We further address the cleaning of a probabilistic database, in order to improve top-k query quality. Cleaning involves the reduction of ambiguity associated with the database entities. For example, the uncertainty of a temperature value acquired from a sensor can be reduced, or cleaned, by requesting its newest value from the sensor. While this 'cleaning operation' may produce a better query result, it may involve a cost and fail. We investigate the problem of selecting entities to be cleaned under a limited budget. Particularly, we propose an optimal solution and several heuristics. Experiments show that the greedy algorithm is efficient and close to optimal. © 2013 IEEE.published_or_final_versio
Optimal-Location-Selection Query Processing in Spatial Databases
Abstract—This paper introduces and solves a novel type of spatial queries, namely, Optimal-Location-Selection (OLS) search, which has many applications in real life. Given a data object set DA, a target object set DB, a spatial region R, and a critical distance dc in a multidimensional space, an OLS query retrieves those target objects in DB that are outside R but have maximal optimality. Here, the optimality of a target object b 2 DB located outside R is defined as the number of the data objects from DA that are inside R and meanwhile have their distances to b not exceeding dc. When there is a tie, the accumulated distance from the data objects to b serves as the tie breaker, and the one with smaller distance has the better optimality. In this paper, we present the optimality metric, formalize the OLS query, and propose several algorithms for processing OLS queries efficiently. A comprehensive experimental evaluation has been conducted using both real and synthetic data sets to demonstrate the efficiency and effectiveness of the proposed algorithms. Index Terms—Query processing, optimal-location-selection, spatial database, algorithm. Ç
Entropy, Triangulation, and Point Location in Planar Subdivisions
A data structure is presented for point location in connected planar
subdivisions when the distribution of queries is known in advance. The data
structure has an expected query time that is within a constant factor of
optimal. More specifically, an algorithm is presented that preprocesses a
connected planar subdivision G of size n and a query distribution D to produce
a point location data structure for G. The expected number of point-line
comparisons performed by this data structure, when the queries are distributed
according to D, is H + O(H^{2/3}+1) where H=H(G,D) is a lower bound on the
expected number of point-line comparisons performed by any linear decision tree
for point location in G under the query distribution D. The preprocessing
algorithm runs in O(n log n) time and produces a data structure of size O(n).
These results are obtained by creating a Steiner triangulation of G that has
near-minimum entropy.Comment: 19 pages, 4 figures, lots of formula
On R-trees with low query complexity
The R-tree is a well-known bounding-volume hierarchy that
is suitable for storing geometric data on secondary memory. Unfortu-
nately, no good analysis of its query time exists. We describe a new algo-
rithm to construct an R-tree for a set of planar objects that has provably
good query complexity for point location queries and range queries with
ranges of small width. For certain important special cases, our bounds
are optimal. We also show how to update the structure dynamically, and
we generalize our results to higher-dimensional spaces
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