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Color-coding

Noga Alon, Raphael Yuster, Uri Zwick
1995 Journal of the ACM  
We describe a novel randomized method, the method of color-coding for finding simple paths and cycles of a specified length k, and other small subgraphs, within a given graph G = (V, E).  ...  Using the color-coding method we obtain, in particular, the following new results: • For every fixed k, if a graph G = (V, E) contains a simple cycle of size exactly k, then such a cycle can be found in  ...  In the next section we describe a simplified version of the color-coding method called the method of random orientations. The basic color-coding method is described in Section 3.  ... 
doi:10.1145/210332.210337 fatcat:xcxlixjrcbbrxkgn2lamsijyke

Color-coding

Noga Alon, Raphy Yuster, Uri Zwick
1994 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94  
We describe a novel randomized method, the method of color-coding for finding simple paths and cycles of a specified length k, and other small subgraphs, within a given graph G = (V, E).  ...  Using the color-coding method we obtain, among others, the following new results: * • If a graph G = (V, E) contains a subgraph isomorphic to a bounded tree-width graph H = (V H , E H ) where |V H | =  ...  In the next section we describe a simplified version of the color-coding method called the method of random orientations. The basic color-coding method is described in Section 3.  ... 
doi:10.1145/195058.195179 dblp:conf/stoc/AlonYZ94 fatcat:7escc6ce2nfmtowkqhrauzn3ae

Doubled Color Codes [article]

Sergey Bravyi, Andrew Cross
2015 arXiv   pre-print
Our approach is based on a doubled version of the 2D color code.  ...  Doubled color codes are promising candidates for the experimental demonstration of logical gates since they do not require state distillation.  ...  We refer to the new family of codes as doubled color code since the construction relies on taking two copies of the regular color codes.  ... 
arXiv:1509.03239v1 fatcat:evjb7gd7kraexif766svfqqdfy

Parallel color-coding

George M. Slota, Kamesh Madduri
2015 Parallel Computing  
Color-coding can be in general applied to finding any subgraphs with a bounded tree-width in polynomial time, by executing the color-coding algo-60 rithm with the tree decomposition of the subgraph [1]  ...  Another application of color-coding that is not included in this work is for finding cycles of length k.  ...  Color-coding was first proposed by Alon, Yuster, and Zwick [1] .  ... 
doi:10.1016/j.parco.2015.02.004 fatcat:hbut56hljnalzmjdfzw5aof7eq

Color Image Coding by Colorization Approach

Takahiko Horiuchi, Shoji Tominaga
2008 EURASIP Journal on Image and Video Processing  
Recommended by Konstantinos Plataniotis This paper proposes a new color image coding scheme called "colorization image coding."  ...  The luminance image component is coded by a lossy coding technique and the chrominance image component is stored as color seeds. The decoding is performed by the colorization algorithm.  ...  This paper applies the colorization technique to image data coding, and we call the technique "colorization image coding."  ... 
doi:10.1155/2008/158273 fatcat:2xc6suw6xjbpjbtf6fhhx4qlyi

Qudit color codes and gauge color codes in all spatial dimensions

Fern H. E. Watson, Earl T. Campbell, Hussain Anwar, Dan E. Browne
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
For completeness, we show explicitly that the qudit color codes generalize to gauge color codes, and share the many of the favorable properties of their qubit counterparts.  ...  We show that the qudit color code can support the qudit analogues of these gates, and show that in higher spatial dimensions a color code can support a phase gate from higher levels of the Clifford hierarchy  ...  Acknowledgements DEB would like to thank Hector Bombin and Ben Brown for helpful and elucidatory discussions on color codes and gauge color codes.  ... 
doi:10.1103/physreva.92.022312 fatcat:rdabbs24nre5znjjoco2xdl2ey

COLOR-CODING CHROMEVALENT ANTIGEN

M. Gershman
1963 Journal of Bacteriology  
This method suggests the use of color-coded composites of heterologous genera for the multiplescreening of suspected serum samples. The root-nodule bacteria vary in their response to vitamins.  ...  colored formazans.  ... 
doi:10.1128/jb.86.4.883-884.1963 fatcat:fmp6g5enpzhnrca2pe6r24lq3q

Extended quantum color coding

A. Hayashi, T. Hashimoto, M. Horibe
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
The quantum color coding scheme proposed by Korff and Kempe (quant-ph/0405086) is easily extended so that the color coding quantum system is allowed to be entangled with an extra auxiliary quantum system  ...  It is shown that in the extended scheme we need only ∼ 2√(N) quantum colors to order N objects in large N limit, whereas ∼ N/e quantum colors are required in the original non-extended version.  ...  to order N objects in the extended quantum color coding scheme.  ... 
doi:10.1103/physreva.71.012326 fatcat:ngvdzw6dwnhtrbbt4r6l5lomg4

Unfolding the color code

Aleksander Kubica, Beni Yoshida, Fernando Pastawski
2015 New Journal of Physics  
Moreover, for the d-dimensional color code with d+1 boundaries of d+1 distinct colors, we find that the code is equivalent to multiple copies of the d-dimensional toric code which are attached along a  ...  The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation.  ...  Brief introduction to the color code and the toric code We begin by briefly reviewing the construction of the topological color code and the toric code.  ... 
doi:10.1088/1367-2630/17/8/083026 fatcat:yhsovdu7hvf5pis7bvnn4bp2ou

Hyperbolic quantum color codes [article]

Eduardo Brandani da Silva, Waldir Silva Soares Jr
2018 arXiv   pre-print
We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before.  ...  Current work presents a new approach to quantum color codes on compact surfaces with genus g ≥ 2 using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations.  ...  Quantum Color Codes The Quantum Color Codes were introduced by Bombim and Martin-Delgado in [10] .  ... 
arXiv:1804.06382v1 fatcat:onqo3h5vqvcnti4a6mqepgvntm

Task-Driven Color Coding

Christian Tominski, Georg Fuchs, Heidrun Schumann
2008 2008 12th International Conference Information Visualisation  
Color coding is a widely used visualization method for scalar data.  ...  In this paper, we describe a color coding approach that accounts for the different tasks users might pursue when analyzing data.  ...  color coding.  ... 
doi:10.1109/iv.2008.24 dblp:conf/iv/TominskiFS08 fatcat:kmqsuly5dfesfe5whtueejiktm

COLOR-CODING CHROMEVALENT ANTIGEN

M GERSHMAN
1963 Journal of Bacteriology  
This method suggests the use of color-coded composites of heterologous genera for the multiplescreening of suspected serum samples. The root-nodule bacteria vary in their response to vitamins.  ...  colored formazans.  ... 
pmid:14066492 pmcid:PMC278532 fatcat:syorxbs55jfzhbz5u4l7vy4csy

Mixing Color Coding-Related Techniques [article]

Meirav Zehavi
2015 arXiv   pre-print
Narrow sieves, representative sets and divide-and-color are three breakthrough color coding-related techniques, which led to the design of extremely fast parameterized algorithms.  ...  This includes: (a) a mix of representative sets and narrow sieves; (b) a faster computation of representative sets under certain separateness conditions, mixed with divide-and-color and a new technique  ...  Strategies for mixing color coding-related techniques, described in Section 3.  ... 
arXiv:1410.5062v3 fatcat:6se2mu7tkjbylmmtt5ajuwpruu

Color Shrinkage For Sparse Coding Of Color Images

T. Komatsu, Takahiro Saito, Yasutaka Ueda
2010 Zenodo  
CONCLUSIONS As a basic tool for the sparse coding of a color image, we present new hard color-shrinkage that utilizes inter-channel color crosscorrelations directly in the primary color space.  ...  The linear color shrinkage is constructed as a solution of a linear simultaneous equation with three unknowns, r, g, b, but is not useful for the sparse coding of a color image.  ... 
doi:10.5281/zenodo.41868 fatcat:ki7hztxen5b5rmnmhjhphl45sm

Colored Prüfer Codes for $k$-Edge Colored Trees

Manwon Cho, Dongsu Kim, Seunghyun Seo, Heesung Shin
2004 Electronic Journal of Combinatorics  
A combinatorial bijection between $k$-edge colored trees and colored Prüfer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number $k(n-2)!  ...  {nk-n\choose n-2}$ of $k$-edge colored trees with $n$ vertices.  ...  An array like the above is called a colored Prüfer code, since its first row is a Prüfer code and its second row can be interpreted as an edge-coloring. the electronic journal of combinatorics 11 (2004  ... 
doi:10.37236/1851 fatcat:mektamd4undhplspnecyhzpa2m
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