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Approximate Colored Range Queries [chapter]

Ying Kit Lai, Chung Keung Poon, Benyun Shi
2005 Lecture Notes in Computer Science  
In this paper, we formulate a class of colored range query problems to model the multi-dimensional range queries in the presence of categorical information.  ...  By applying appropriate sketching techniques on our framework, we obtained efficient data structures that provide approximate solutions to these problems.  ...  Note that for f = sum, the weighted and unweighted colored range-f queries are just ordinary range sum and range count queries (without colors) respectively.  ... 
doi:10.1007/11602613_37 fatcat:hq6iofpfrva6xckd3pz7pre43e

Approximate colored range and point enclosure queries

Ying Kit Lai, Chung Keung Poon, Benyun Shi
2008 Journal of Discrete Algorithms  
In this paper, we formulate two classes of problems, the colored range query problems and the colored point enclosure query problems to model multi-dimensional range and point enclosure queries in the  ...  Based on a new framework of combining sketching techniques and traditional data structures, we obtain two sets of results in solving the problems approximately and efficiently.  ...  Approximate colored range queries In this section, we consider the problem of colored range queries. We start by illustrating our methodology using 1-dimensional range queries.  ... 
doi:10.1016/j.jda.2007.10.001 fatcat:4vb3zathmbbxllxqwtiw5letda

Succinct Color Searching in One Dimension

Hicham El-Zein, J. Ian Munro, Yakov Nekrich, Marc Herbstritt
2017 International Symposium on Algorithms and Computation  
Thus we show, somewhat counterintuitively, that it is not necessary to store colors of points in order to answer approximate color counting queries.  ...  A color reporting query asks for the list of distinct colors that occur in a query interval [a, b] and a color counting query asks for the number of distinct colors in [a, b].  ...  Approximate Color Range Counting In this section we present a data structure that uses B(n, m) + O(n) + o(B(n, m)) bits of space and answers approximate color counting queries in constant time.  ... 
doi:10.4230/lipics.isaac.2017.30 dblp:conf/isaac/El-ZeinMN17 fatcat:qbv6elklgngndhj6ggvh2izeua

Approximate Range Counting Revisited [article]

Saladi Rahul
2017 arXiv   pre-print
We study range-searching for colored objects, where one has to count (approximately) the number of colors present in a query range.  ...  Most of the results are obtained via reductions to the approximate uncolored version, and improved data-structures for them.  ...  Colored Orthogonal Range Search in R 2 To illustrate an application of Reduction-I, we study the approximate colored counting query for orthogonal range search in R 2 . Theorem 5.  ... 
arXiv:1512.01713v3 fatcat:i3bck3vanbbqnfmittuwsazg5q

Categorical Range Reporting with Frequencies

Arnab Ganguly, J. Ian Munro, Yakov Nekrich, Rahul Shah, Sharma V. Thankachan, Michael Wagner
2019 International Conference on Database Theory  
Next we turn to an approximate version of this problem: report all colors σ that appear in the query range; for every reported color, we provide a constant-factor approximation on its frequency.  ...  Our goal is to pre-process a set of colored points into a data structure, so that given a query range Q, we can report all colors that appear in Q, along with their respective frequencies.  ...  In the related approximate range counting problem, we must approximate the number of point within the query range.  ... 
doi:10.4230/lipics.icdt.2019.9 dblp:conf/icdt/GangulyMNST19 fatcat:3jkmhuqlnza75dfrgj6mqoto4i

Significant-Presence Range Queries in Categorical Data [chapter]

Mark de Berg, Herman J. Haverkort
2003 Lecture Notes in Computer Science  
color intersecting the query range.  ...  Our main results are on an approximate version of this problem, where we are also allowed to report those colors for which a fraction (1 − ε)τ intersects the query range, for some fixed ε > 0.  ...  objects of that color intersect the query range.  ... 
doi:10.1007/978-3-540-45078-8_40 fatcat:eapwiynl6fa5zfgyt3tudpxz3m

Chromatic k-Nearest Neighbor Queries [article]

Thijs van der Horst, Maarten Löffler, Frank Staals
2022 arXiv   pre-print
Since these query times are still fairly large we also consider approximations.  ...  query times ranging between Õ(n^1/2ε^-3/2) and Õ(n^1/2ε^-5/2) in ℝ^2 using near-linear space (ignoring polylogarithmic factors).  ...  is unclear how to use approximate solutions to k-NN queries (that is, approximate ranges) and still obtain guarantees on the approximation factor of our ε-approximate chromatic k-NN queries.  ... 
arXiv:2205.00277v1 fatcat:2wa7rvkm7rbwhazk4p7vr7h7uy

Fully Retroactive Approximate Range and Nearest Neighbor Searching [article]

Michael T. Goodrich, Joseph A. Simons
2011 arXiv   pre-print
We support, for any small constant ϵ>0, (1+ϵ)-approximate range reporting queries at any point in the timeline in O( n + k) time, where k is the output size.  ...  We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting.  ...  Theorem 3.1 (Fully-Retroactive Approximate Range Queries).  ... 
arXiv:1109.0312v1 fatcat:h2edpeoy4ba2bpbqi3fyzxga6y

Colored range queries and document retrieval

Travis Gagie, Juha Kärkkäinen, Gonzalo Navarro, Simon J. Puglisi
2013 Theoretical Computer Science  
We then show how (approximate) colored top-k queries can be reduced to (approximate) range-mode queries on subsequences, yielding the first efficient data structure for this problem.  ...  In this paper we give improved time and space bounds for three important one-dimensional colored range queries -colored range listing, colored range top-k queries and colored range counting -and, thus,  ...  color frequencies), colored range top-k queries, and colored range counting.  ... 
doi:10.1016/j.tcs.2012.08.004 fatcat:bc36cwxqovd5jflbruydfyfmia

Colored Range Queries and Document Retrieval [chapter]

Travis Gagie, Gonzalo Navarro, Simon J. Puglisi
2010 Lecture Notes in Computer Science  
We then show how (approximate) colored top-k queries can be reduced to (approximate) range-mode queries on subsequences, yielding the first efficient data structure for this problem.  ...  In this paper we give improved time and space bounds for three important one-dimensional colored range queries -colored range listing, colored range top-k queries and colored range counting -and, thus,  ...  color frequencies), colored range top-k queries, and colored range counting.  ... 
doi:10.1007/978-3-642-16321-0_7 fatcat:ego734iu7zd2xnvrnwvip5k2ny

Low space data structures for geometric range mode query

Stephane Durocher, Hicham El-Zein, J. Ian Munro, Sharma V. Thankachan
2015 Theoretical Computer Science  
Given a query range , the geometric range mode query problem asks to report the most frequent color (i.e., a mode) of the multiset of colors corresponding to points in S ∩ Q.  ...  ., d ≥ 2) with O(s n + (n/∆) 2d ) space and O(∆ · t n ) query time, where s n and t n denote the space and query time of a data structure that supports orthogonal range counting queries on the set S.  ...  Definition 1 ( 1 Range Mode Query) Given S, a set of n points in an [n] d grid, such that each point is a assigned a color (there can be at most n colors).  ... 
doi:10.1016/j.tcs.2015.03.011 fatcat:ll763b7nxbfsfnikyb4qwsp2e4

Grouping And Indexing Color Features For Efficient Image Retrieval

M. V. Sudhamani, C. R. Venugopal
2007 Zenodo  
A JAVA based query engine supporting query-by- example is built to retrieve images by color.  ...  For similarity retrieval, each representative color in the query image or region is used independently to find regions containing that color. The results of these methods are compared.  ...  Searching for the individual colors can be done very efficiently in a 3-D color space. We consider here only fixed range queries in which the range value limits the search range.  ... 
doi:10.5281/zenodo.1331774 fatcat:l65nzj4pybekjkyrmd4id3o74a

VisDB

Daniel A. Keim, Hans-Peter Kriegel
1995 Proceedings of the 1995 ACM SIGMOD international conference on Management of data - SIGMOD '95  
Users may, for example, interactively change the query ranges, highlight corresponding pixels in different windows, use a projection of the visual representation to specific color ranges, or access the  ...  The colorscale maps correct answers to yellow and approximate results to colors ranging from green, blue, and red to almost black (decreasing lightness denotes an increasing distance from the correct answers  ... 
doi:10.1145/223784.223895 dblp:conf/sigmod/KeimK95 fatcat:u53ezruikzefvbbvvx7j2gll6e

VisDB: database exploration using multidimensional visualization

D.A. Keim, H.-P. Kriegel
1994 IEEE Computer Graphics and Applications  
By arranging and coloring the pixels according to the relevance of the data items with respect to the query, the user gets a visual impression of the resulting data set.  ...  Using sliders for each condition of the query, the user may change the query dynamically and receives immediate feedback from the visual representation of the resulting data set.  ...  data values corresponding to some 'selected color range'.  ... 
doi:10.1109/38.310723 fatcat:w7dqfy2r4bgbjf33nithix6cci

Colored range closest-pair problem under general distance functions [article]

Jie Xue
2018 arXiv   pre-print
the query range.  ...  We design efficient (1+ε)-approximate CRCP data structures for orthogonal queries in R^2, where ε>0 is a pre-specified parameter.  ...  points with different colors (or the top-2 points for short) in the query range.  ... 
arXiv:1807.09977v1 fatcat:kklmfli4qzekhpvnccsyrknhxi
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