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Decomposition of multiple coverings into many parts
2007
Proceedings of the twenty-third annual symposium on Computational geometry - SCG '07
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Let m(k) denote the smallest positive integer m such that any m-fold covering of the plane with axis-parallel unit squares splits into at least k coverings. ...
Is it true that if every point of the plane belongs to the range of many sensors, then we can monitor the plane for a long time without running out of power? ...
can be decomposed into simpler parts. ...
doi:10.1145/1247069.1247096
dblp:conf/compgeom/PachT07
fatcat:s2m6mveyxffe7puww6iadm6q3m
Decomposition of multiple coverings into many parts
2009
Computational geometry
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Let m(k) denote the smallest positive integer m such that any m-fold covering of the plane with axis-parallel unit squares splits into at least k coverings. J. Pach [J. ...
Pach, Covering the plane with convex polygons, Discrete and Computational Geometry 1 (1986) [73][74][75][76][77][78][79][80][81] showed that m(k) exists and gave an exponential upper bound. ...
can be decomposed into simpler parts. ...
doi:10.1016/j.comgeo.2008.08.002
fatcat:3uqhcx4gnjfdbcxlk34yh6q6oe
Decomposition of complete tripartite graphs into 5-cycles using the graph adjacency matrix
[article]
2021
arXiv
pre-print
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The problem of decomposing a complete tripartite graph into 5-cycles was first proposed in 1995 by Mahmoodian and Mirzakhani and since then many attempts have been made to decompose such graphs into 5- ...
Such attempts were partially successful but parts of the problem still remain open. ...
So, K r,s,t where s, t are multiples of 5 is proved to admit a 5-cycle decomposition unless when 2.27r ≤ t < 3r. The above theorems solve many of the cases in this gap. ...
arXiv:1910.06385v3
fatcat:6ftbzzyaurbuvflmte66w7zcei
Recovering rearranged cancer chromosomes from karyotype graphs
[article]
2019
bioRxiv
pre-print
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We then demonstrate that Eulerian decomposition of the cancer karyotype graphs is not always unique and present the Consistent Contig Covering Problem (CCCP) of recovering unambiguous cancer contigs from ...
Recently it became possible to reconcile both of these types of large-scale variations into a karyotype graph representation of the rearranged cancer genomes. ...
This paper was in part inspired by programming solutions to the problem "Cancer and Chromosome Rearrangements" on the Bioinformatics Contest 2019 https://bioinf.me/en/contest/2019. ...
doi:10.1101/831057
fatcat:exn5iiq7dndihhrepvvzmuvmsy
Decomposing the real line into Borel sets closed under addition
[article]
2014
arXiv
pre-print
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We consider decompositions of the real line into pairwise disjoint Borel pieces so that each piece is closed under addition. How many pieces can there be? ...
We also investigate various versions: what happens if we drop the Borelness requirement, if we replace addition by multiplication, if the pieces are subgroups, if we partition (0,∞), and so on. ...
Then G is clearly countable and it is easy to see that the orbits of G form a partition of R into c many countable sets all of which are closed under addition and multiplication. ...
arXiv:1406.0701v2
fatcat:bcat7sc32bdvhhtu7bemuqnkwe
On the design of relational database schemata
1981
ACM Transactions on Database Systems
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A decomposition algorithm is presented which (1) permits decomposition of complex relations into simple, well-defined primitives, (2) preserves all the original information, and (3) minimizes redundancy ...
Admissibility of covers and validation of results are also discussed, and it is shown how these concepts may be used to improve the design of 3NF schemata. ...
ACKNOWLEDGMENT The authors would like to express their sincere appreciation to the referees whose incisive critiques and comments have played an important role in the development of this paper. ...
doi:10.1145/319540.319542
fatcat:fnl46hfzjfekvl3qwnvpjcmsuu
Manufacturing feature recognition from solid models: a status report
2000
IEEE Transactions on Robotics and Automation
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Automated feature recognition has been an active research area in solid modeling for many y ears and is considered to be a critical component for integration of Computer-Aided Design and Computer-Aided ...
Rather than giving an exhaustive survey, w e focus on the three of the major algorithmic approaches for feature recognition: graph-based algorithms, volumetric decomposition techniques, and hint-based ...
Further, any opinions, ndings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re ect the views of the National Science Foundation or the other ...
doi:10.1109/70.897789
fatcat:bllpfvkznjbkbj3h37bmrswnbq
A new approach for explaining Rhind's Recto – and its utility in teaching
2015
Teaching Mathematics and Computer Science
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The Recto is a table in the Rhind Mathematical Papyrus (RMP) of ancient Egypt containing the unit fraction decompositions of fractions 2/n (3 ≤ n ≤ 101, n odd). ...
The fact that in some other sources of Egyptian mathematics decompositions different from those in Recto exist makes the problem more difficult. ...
The boldface characters of the results show how many parts the two units be divided into to reach 2. ...
doi:10.5485/tmcs.2004.0064
fatcat:tmyvggk6v5buzolvnotmxzr4ei
New steerable pyramid steganography algorithm resistant to the Fisher Linear Discriminant steganalysis
2008
Annales UMCS Informatica
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The main part of the paper is the description of the conducted research and the results of FLD steganalysis of stegoimages produced by the new steganography algorithm. * ...
This paper describes a new steganography algorithm based on a steerable pyramid transform of a digital image and the steganalysis of the existence of secret messages hidden by this new method. ...
The decomposition splits the frequency space of the image into multiple scales and three orientations: vertical, horizontal and diagonal. ...
doi:10.2478/v10065-008-0025-1
fatcat:v2pjmvnx5ndllhhbbzqzr3mh5q
Generalized cylinder decomposition
2015
ACM Transactions on Graphics
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The over-completeness of the cylinder covers ensures a conservative buildup of the cylindrical parts, leaving the final decision on decomposition to global optimization. ...
Our decomposition algorithm progressively builds local to non-local cylinders, which form over-complete covers of the input shape. ...
This work was supported in part by NSFC (61522213, 61232011, 61528208, 61379090) ...
doi:10.1145/2816795.2818074
fatcat:v4o2kscp7rbkpef3pl7ysh5wum
Minimal Decomposition of a Digital Surface into Digital Plane Segments Is NP-Hard
[chapter]
2006
Lecture Notes in Computer Science
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This paper deals with the complexity of the decomposition of a digital surface into digital plane segments (DPS for short). ...
The proof is based on a polynomial reduction of any instance of the well-known 3-SAT problem to an instance of the digital surface decomposition problem. ...
The minimal number of DPS needed to cover the idle part will be fixed for each basic element, and any decomposition of this part into maximal DPS will exactly cover the same voxels, with no possible extension ...
doi:10.1007/11907350_57
fatcat:fcgttwui7jdm7ltipx5fz6wy3u
Recovering rearranged cancer chromosomes from karyotype graphs
2019
BMC Bioinformatics
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We then demonstrate that Eulerian decomposition of the cancer karyotype graphs is not always unique and present the Consistent Contig Covering Problem (CCCP) of recovering unambiguous cancer contigs from ...
Recently it became possible to reconcile both of these types of large-scale variations into a karyotype graph representation of the rearranged cancer genomes. ...
Raphael for thoughtful and productive discussions that helped to shape the original RCK theoretical framework, the observed graph decomposition research problems and ways to address them. ...
doi:10.1186/s12859-019-3208-4
pmid:31842730
pmcid:PMC6915857
fatcat:fdhdhwmnnbdubgor5vxestnveq
Comparative analysis of different polarimetric target decompositions for Land cover Classification
2020
Proceedings of the Indian National Science Academy
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Many studies revealed Synthetic Aperture Radar data (SAR) backscattering is a very useful technique in identification of soil contents and various land cover types. ...
and Multiple Component Scattering Model (MCSM), for land cover classification using C-band SAR data. ...
Double bounce scattering fails to produce sufficient separation between classes in many of the decompositions. ...
doi:10.16943/ptinsa/2020/157318
fatcat:wkf7ag3z6fh7tdma2d4o554ln4
Sharp bounds for decompositions of graphs into completer-partite subgraphs
1996
Journal of Graph Theory
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If G is a graph on n vertices and r 2 2, w e let m,(G) denote the minimum number of complete multipartite subgraphs, with r or fewer parts, needed to partition the edge set, f(G). ...
We conclude with a short proof of the known eigenvalue bound m,(G) 2 max{n+(G), n-(G)/(r -I)}, and show that equality holds if G = G(r, k). ...
Huang [9] has examined decompositions of K , into complete r-partite subgraphs that have precisely r nonempty vertex parts. ...
doi:10.1002/(sici)1097-0118(199604)21:4<393::aid-jgt4>3.0.co;2-k
fatcat:75h3ajd3jzez7jz5j5mno2jgpi
Page 1833 of The Lancet Vol. 174, Issue 4426
[page]
1908
The Lancet
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
to an enormous extent and gradually, by its continued growth and lengthening and multiplication, to pervade farther and farther into the ham. ...
We have, then, sufficient reason for maintaining that the microbe, by its growth, multiplication, and chemical activity, is the real cause of the changes that characterise the taint or decomposition of ...
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