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Space Efficient Two-Dimensional Orthogonal Colored Range Counting [article]

Younan Gao, Meng He
2021 arXiv   pre-print
In the two-dimensional orthogonal colored range counting problem, we preprocess a set, P, of n colored points on the plane, such that given an orthogonal query rectangle, the number of distinct colors  ...  of the points contained in this rectangle can be computed efficiently.  ...  tradeoff for 2D orthogonal colored range counting.  ... 
arXiv:2107.02787v1 fatcat:4onlwob3ofa5pfgsusijeuky4a

Space Efficient Two-Dimensional Orthogonal Colored Range Counting

Younan Gao, Meng He, Petra Mutzel, Rasmus Pagh, Grzegorz Herman
2021
In the two-dimensional orthogonal colored range counting problem, we preprocess a set, P, of n colored points on the plane, such that given an orthogonal query rectangle, the number of distinct colors  ...  of the points contained in this rectangle can be computed efficiently.  ...  tradeoff for 2D orthogonal colored range counting.  ... 
doi:10.4230/lipics.esa.2021.46 fatcat:nzkhiwwaqfewhpmz5dyxtik4fm

Further Results on Colored Range Searching

Timothy M. Chan, Qizheng He, Yakov Nekrich, Danny Z. Chen, Sergio Cabello
2020 International Symposium on Computational Geometry  
counting queries: report the number of occurrences of every distinct color in a query orthogonal range.  ...  n) space that can report the distinct colors in any query orthogonal range (axis-aligned box) in O(k polyloglog n) expected time, where k is the number of distinct colors in the range, assuming that coordinates  ...  There exists a data structure that uses O(m log m log ε n) words of space and supports 4-sided type-2 range counting queries in O(log n/ log log n + k log log n) time.  ... 
doi:10.4230/lipics.socg.2020.28 dblp:conf/compgeom/ChanHN20 fatcat:67s66uihezctbgjc2zjzfzm42u

Further Results on Colored Range Searching [article]

Timothy M. Chan, Qizheng He, Yakov Nekrich
2020 arXiv   pre-print
distinct color in a query orthogonal range.  ...  For a set of n colored points in three dimensions, we describe randomized data structures with O(n polylogn) space that can report the distinct colors in any query orthogonal range (axis-aligned box) in  ...  There exists a data structure that uses O(m log m log ε n) words of space and supports 4-sided type-2 range counting queries in O(log n/ log log n + k log log n) time.  ... 
arXiv:2003.11604v1 fatcat:gx3dwjegibcs7ehfrvjzvwckca

Searching for Frequent Colors in Rectangles [article]

Marek Karpinski, Yakov Nekrich
2008 arXiv   pre-print
We study a new variant of colored orthogonal range searching problem: given a query rectangle Q all colors c, such that at least a fraction τ of all points in Q are of color c, must be reported.  ...  Acknowledgment We would like to thank Mark de Berg and Herman Haverkort for stimulating discussions and for suggestions concerning the new variant of colored range searching problem.  ...  Colored orthogonal range reporting queries in d dimensions can be answered in O(log n + k) time with a data structure that uses O((n 1+ε )) space [1] , but no efficient pseudo-linear space data structure  ... 
arXiv:0805.1348v1 fatcat:p4fpulfg4zfarnhc4es53zzfju

On Generalized Planar Skyline and Convex Hull Range Queries [chapter]

Nadeem Moidu, Jatin Agarwal, Sankalp Khare, Kishore Kothapalli, Kannan Srinathan
2014 Lecture Notes in Computer Science  
Our solutions are in the pointer machine model, for orthogonal range queries on a static point set. We solve the planar range maxima problem for two-sided, three-sided and four-sided queries.  ...  We achieve a query time of O(log n + c) using O(n) space for the two-sided case, where n denotes the number of stored points and c the number of colors reported.  ...  a query range we can efficiently report the distinct colors in that range.  ... 
doi:10.1007/978-3-319-04657-0_6 fatcat:2vcnyow6fnbyfbotktu7fmyuoy

Colored Range Searching on Internal Memory [chapter]

Haritha Bellam, Saladi Rahul, Krishnan Rajan
2012 Lecture Notes in Computer Science  
This leads to the need for more sophisticated queries and hence novel data structures and algorithms such as the orthogonal colored range searching (OCRS) problem which is a generalized version of orthogonal  ...  range searching.  ...  ] ⊆ IR d , all the points of S lying inside q need to be reported/counted efficiently".  ... 
doi:10.1007/978-3-642-29035-0_8 fatcat:pbzqrv2ku5fs7jh5pe2gesyymy

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.  ...  The problems studied mostly involve orthogonal range-searching in two and three dimensions, and the dual setting of rectangle stabbing by points.  ...  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

DATA STRUCTURES FOR RANGE-AGGREGATION OVER CATEGORIES

SALADI RAHUL, PROSENJIT GUPTA, K. S. RAJAN
2011 International Journal of Foundations of Computer Science  
that given a query orthogonal range q (e.g. hyperbox/point), we can report efficiently for each distinct color c of the points in S ∩ q, the tuple c, F (c) where F (c) is a function (e.g. weighted sum  ...  We solve instances of a general class of problems defined as follows: Preprocess a set S of possibly weighted colored geometric objects (e.g. points/orthogonal segments/rectangles) in IR d , d ≥ 1 such  ...  The goal is to preprocess S such that given a query orthogonal range q, we can report efficiently for each distinct color c of the objects in S ∩ q, the tuple c, F (c) where F (c) is a function of the  ... 
doi:10.1142/s0129054111008982 fatcat:2knlly72jfgnvmpmyw36dfo6pq

Single photon emitters based on Ni/Si related defects in single crystalline diamond

D. Steinmetz, E. Neu, J. Meijer, W. Bolse, C. Becher
2011 Applied physics B  
In addition, some color centers feature stable and bright emission with saturation count rates up to 78kcounts/s whereas others show fluctuating count rates and three-level blinking.  ...  two-level, single-dipole systems whereas other centers exhibit three levels and contributions from two orthogonal dipoles.  ...  Fig. 4 4 Emission spectra of four Ni/Si related color centers in the spectral range 765 -775 nm. The spectra can be fitted with one or two Lorentz peak functions.  ... 
doi:10.1007/s00340-011-4402-x fatcat:re5m2okmfjaldk6i4hexfguojy

Low space data structures for geometric range mode query

Stephane Durocher, Hicham El-Zein, J. Ian Munro, Sharma V. Thankachan
2015 Theoretical Computer Science  
., 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.  ...  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.  ...  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

Content‐based image retrieval using Gaussian–Hermite moments and firefly and grey wolf optimization

Yasasvy Tadepalli, Meenakshi Kollati, Swaraja Kuraparthi, Padmavathi Kora, Anil Kumar Budati, Lakshmi Kala Pampana
2021 CAAI Transactions on Intelligence Technology  
clustering ​and Color descriptor wavelet‐based texture descriptor retrieval technique.  ...  When these optimized weights are applied, the proposed algorithm shows better precision/recall and efficiency than other techniques such as exact legendre moments, Region‐based image retrieval, K‐means  ...  The main reason of introducing orthogonality in Gaussian-Hermite polynomials are stable and fast numerical implementation, avoidance of high dynamic range of moment values that may lead to loss of precision  ... 
doi:10.1049/cit2.12040 doaj:20b5a29a4e424a1998a2857938ca795c fatcat:ue5pgr6v6fa45igumwbzrtuxlm

Optimal Private Halfspace Counting via Discrepancy [article]

S. Muthukrishnan, Aleksandar Nikolov
2012 arXiv   pre-print
This approach also yields a lower bound of Ω(( n)^d-1) for (ϵ, δ)-differentially private orthogonal range counting in d dimensions, the first known superconstant lower bound for this problem.  ...  For the upper bound, we use an approach inspired by partial coloring methods for proving discrepancy upper bounds, and obtain (ϵ, δ)-differentially private algorithms for range counting with polynomially  ...  Their algorithm is not computationally efficient, but they gave efficient algorithms with comparable guarantees for the interval range counting and halfspace range counting problems.  ... 
arXiv:1203.5453v1 fatcat:ffyswtu3prb5vpavhxhcfiouka

Interference Aware Channel Assignmnet Using Edge Coloring in Multi-Channel Multi-Radio Wireless Mesh Networks [article]

Sarasvathi V, N.CH.S.N.Iyengar, Snehanshu Saha
2013 arXiv   pre-print
In this paper, we represent the channel assignment as a graph edge coloring problem using POC.  ...  Many algorithms and methods have been developed for channel assignment to maximize network throughput using orthogonal channels.  ...  The physical distance between two nodes is 200m in square topology; the transmission range is 250m for all the nodes and the interference range is 550m.  ... 
arXiv:1305.0866v2 fatcat:7uzapblbbbemzgd4drjbcvg5de

Page 5028 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
by g can be reported efficiently or the number of such colors can be counted efficiently.  ...  “To obtain our more efficient solutions, we also develop some auxiliary results concerning batched range searching where the ranges are congruent discs or annuli.  ... 
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