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Encyclopedia Source Summary
DJ Oneil (G01)
Nearest Neighbor Problem
Key Words:
nearest neighbor, all-nearest-neighbor, all-k-nearest neighbor, Ann, Aknn, range query
Comments:
Given n points and a query point, the nearest neighbor problem finds the closest point to
the query point (O(n)). This problem is usually extended to find All-k-nearest-neighbors
where the k nearest neighbors of every point in the set are found. In spatial database
problems, the nearest neighbor problem is usually used to find the k-nearest-neighbors of
a single query point. There is also some research in finding the nearest neighbors over
time where the elements are moving.
Sources:
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Anany Levitin. Introduction to The Design and Analysis of Algorithms. Addison
Wesley. 2003.
o Provides problem definition.
o Presents the basic algorithm.
Wolfram MathWorld. Jan. 5, 2005. “Nearest Neighbor Problem”. Sept. 29, 2006.
http://mathworld.wolfram.com/NearestNeighborProblem.html
o Provides a concise problem definition.
Chavez, et al… “A Fast Algorithm for the All k Nearest Neighbors Problem in
General Metric Spaces”
o Provides background research information on the topic; brute force, using
Veronoi diagrams, and Delaunay triangulation.
o Proposes faster method that uses an index that can satisfy range queries.
Using a range query, it find the γn elements performing γαn distance
computations, with 0 ≤ α ≤ 1 depending on how good the index searches
the space. An α close to 0 is a costly and an α close to 1 is cheap. The
authors’ method becomes O(n*sqrt(kn)) when α is close to 1 with O(kn)
space required.
Benetis, et al… “Nearest and Reverse Nearest Neighbor Queries for Moving
Objects”. The VLDB Journal. Volume 15, Issue 3. Sept. 2006. Pgs. 229-249.
2006
o Proposes a method for finding the k nearest and reverse k nearest
neighbors of moving objects. The motivation of the paper is the
increasing popularity of new wireless technologies such as remote sensor
networks. It uses previous positions of an object to estimate future
positions.
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Achtert, et al… “Efficient Reverse k-Nearest Neighbor Search in Arbitrary Metric
Spaces”. Proceedings of the 2006 ACM SIGMOD international conference on
Management of data. Chical IL. Pgs. 515-526. 2006.
o Proposes the first approach to the Rknn problem on arbitrary metric spaces
where k is specified at query time.
Hjaltason, et al… “Distance browsing in spatial databases”. Hjaltason, et al…
“Distance browsing in spatial databases”. ACM Transactions on Database Systems.
Volume 24, Issue 2. June 1999. Pgs. 265-318. 1999.
o Compares two algorithms for using an R-tree to ket the k nearest
neighbors.
Census
Key Words:
census
Comments:
A census is the process of obtaining data on every person of some population. In the
statistical sense, this contrasts a sample that is a subset of a population; the population is
the entire set.
Sources:
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Wikipedia. Sept. 28, 2006. “Census”. Sept. 29, 2006.
http://en.wikipedia.org/wiki/Census
o Provides a general definition on the Census.
o Gives summaries on the different ways the census is carried out in
different countries.
Spatial Range Query
Key Words:
spatial query, spatial range query, range search
Comments:
Given an n-point set and a set of points defining a query geometric shape, a spatial range
query finds all points within the defined shape.
Sources:
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Orenstein. “Spatial Query Processing in an Object-Oriented Database System”.
Proceedings of the 1986 ACM SIGMOD international conference on Management of
data. Washington D.C.. Pgs 326-336. 1986.
o Briefly defines the problem.
o Briefly describes attempts to model spatial problems using existing DBMS
implementations and how they are inadequate.
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o Examines the common principles and needs of spatial problems and
proposes a small set of constructs
o Shows how these constructs can be easily implemented in existing DBMS
implementations.
Bentley, et al… “Data Structures for Range Searching”. ACM Computing Surveys.
Volume 11, Issue 4. December 1979. Pgs. 397-409. 1979.
o Investigates the data types commonly used for range queries.
Matousek. Geometric Range Searching. ACM Computing Surveys. Volume 26,
Issue 4. December 1994. Pgs. 422-461. 1994.
o A survey of the algorithms commonly use for spatial queries.
Subramanian, et al… “The P-range tree: a new data structure for range searching in
secondary memory”. Proceedings of the sixt annual ACM-SIAM symposium on
Discrete algorithms. Pgs. 378-387. 1995.
o Proposes a new data structure for range searching in secondary memory.
o Also describes data structures for use in main memory and shows that it is
faster than previously used data structures.
Soheili, et al… “Spatial queries in sensor networks”. Proceedings of the 13th annual
ACM international workshop on Geographic information systems. Bremen,
Germany. SESSION: Sensor Networks. Pgs. 61-70. 2005.
o Proposes a way to perform spatial queries using sensor network
information and devices within the low power and bandwidth constraints
of the devices.
Das, et al… “Approximation techniques for spatial data”. Proceedings of the 2004
ACM SIGMOD international conference on Management of data. Paris, France.
SESSION: Research sessions: spatial data. Pgs. 695-706. 2004.
o Proposes an approximation technique for spatial queries.
o Discusses some of the drawbacks of current uses of histograms and/or
sampling.