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Balanced Interval Coloring

Antonios Antoniadis, Falk Hueffner, Pascal Lenzner, Carsten Moldenhauer, Alexander Souza, Marc Herbstritt
2011 Symposium on Theoretical Aspects of Computer Science  
We consider the discrepancy problem of coloring n intervals with k colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal.  ...  In an online scenario, where intervals arrive over time and the color has to be decided upon arrival, the maximal difference in the size of color classes can become arbitrarily high for any online algorithm  ...  Clearly, a balanced coloring has to assign opposite colors to the corresponding two intervals of such a pair, and any such assignment yields a balanced coloring.  ... 
doi:10.4230/lipics.stacs.2011.531 dblp:conf/stacs/AntoniadisHLMS11 fatcat:il6thvtc7bephjsemwvwbi6qlm

Balanced Interval Coloring [article]

Antonios Antoniadis and Falk Hüffner and Pascal Lenzner and Carsten Moldenhauer and Alexander Souza
2010 arXiv   pre-print
We consider the discrepancy problem of coloring n intervals with k colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal.  ...  In an online scenario, where intervals arrive over time and the color has to be decided upon arrival, the maximal difference in the size of color classes can become arbitrarily high for any online algorithm  ...  Clearly, a balanced coloring has to assign opposite colors to the corresponding two intervals of such a pair, and any such assignment yields a balanced coloring.  ... 
arXiv:1012.3932v1 fatcat:pzpyaqrbarfc3bvzwdoqx5dgmq

Balanced Independent and Dominating Sets on Colored Interval Graphs [article]

Sujoy Bhore, Jan-Henrik Haunert, Fabian Klute, Guangping Li, Martin Nöllenburg
2020 arXiv   pre-print
We study two new versions of independent and dominating set problems on vertex-colored interval graphs, namely f-Balanced Independent Set (f-BIS) and f-Balanced Dominating Set (f-BDS).  ...  Let G=(V,E) be a vertex-colored interval graph with a color assignment function γ V →{1,...,k} that maps all vertices in G onto k colors.  ...  Conclusions In this paper, we have studied the f -Balanced Independent and Dominating set problem for proper interval graphs.  ... 
arXiv:2003.05289v2 fatcat:v2pzwqys4rdqlb5w3gkcgplfhe

Interval colorings of complete balanced multipartite graphs [article]

Petros A. Petrosyan
2012 arXiv   pre-print
We also prove that if nk is even and (k-1)n≤ t≤ ((3/2)k-1)n-1, then a complete balanced k-partite graph G admits an interval t-coloring.  ...  In this paper we show that a complete balanced k-partite graph G with n vertices in each part is interval colorable if and only if nk is even.  ...  ,n ) for interval colorable complete balanced k-partite graphs K n,...,n .  ... 
arXiv:1211.5311v1 fatcat:djw3fzfug5gitfajuxzz4fpgtq

Balancing Colored Points on a Line by Exchanging Intervals

Atsushi Kaneko, Mikio Kano, Mamoru Watanabe
2017 Journal of Information Processing  
Moreover we extend this result to multi-colored point sets. Keywords: red and blue points, three colored points, colored points on a line, balanced set, moment curve, hamsandwich theorem.  ...  If the number of colors is more than three, we can obtain balanced sets by exchanging two or more intervals of I ∪ J. Theorem 3 Let r ≥ 2 be an integer, and let c 1 , c 2 , . . . , c r be r colors.  ...  Fig. 4 4 Five colored points lie on a line, and X and Y consists of 3 intervals together. Six colored points lie on a line, and X and Y consists of 4 intervals together.  ... 
doi:10.2197/ipsjjip.25.551 fatcat:tr624qccejcihnwr3jvufdxhqi

Geometric Systems of Unbiased Representatives [article]

Aritra Banik, Bhaswar B. Bhattacharya, Sujoy Bhore, Leonardo Martínez-Sandoval
2020 arXiv   pre-print
Furthermore, we study a related problem on determining the size of the largest and smallest balanced intervals for points on the real line with a random distribution and coloring.  ...  An object from is called balanced with respect to B if it contains the same number of points from each color of B.  ...  Other relevant results on balanced coloring of point sets include the balanced island problem studied by Aichholzer et al. [1] , balanced partitions problem for 3-colored planar sets by Bereg et al.  ... 
arXiv:2002.05488v1 fatcat:ryae2jskrjhdfdnudvip35feim

The Integration of Color-Selective Mechanisms in Symmetry Detection

Chia-Ching Wu, Chien-Chung Chen
2017 Scientific Reports  
Similarly, the threshold for the 4-color pattern should be about 0.15 log units lower than for the 1-color pattern.  ...  Given the fourth-power law 1,2-4 , we would expect the observer to detect symmetry in a two-color pattern with a signal-to-noise ratio of 0.84*k/2 in each color.  ...  non-target interval, including the balancing control and the mask, m nt j E  , ' , was zero.  ... 
doi:10.1038/srep42972 pmid:28230091 pmcid:PMC5322352 fatcat:dpy7uu5cdfbuplq7e5bobdgrxm

Page 24 of American Childhood Vol. 10, Issue 2 [page]

1924 American Childhood  
Pupils suggest change of position or attitude and interval in the arrangement made. Draw these arrangements, coloring with one standard eolor. Draw examples of axial balance in art.  ...  Discuss progression of interval, direction, and SIZe, and arrange units to illustrate each and 37, Plate II. VItl Draw and color some of the arrange- ments in axial balanee.  ... 

Design as a Science

Denman W. Ross
1901 Proceedings of the American Academy of Arts and Sciences  
The greatest possible interval in the color scale is, as I have said, the interval of 180?, the interval between opposite colors of the circle.  ...  When it comes to the consideration of color intervals we have to think not only of the interval between one color and another in the spectrum scale, but, also, of the interval between  ... 
doi:10.2307/20021036 fatcat:pqu7woa3bven7i7oax2i7gk6bu

Page 863 of Daedalus Vol. 36, Issue 21 [page]

1901 Daedalus  
The greatest possible interval in the color scale is, as I have said, the interval of 180°, the interval between opposite colors of the circle. These colors are known as complementaries.  ...  The relation of the complemen- tary colors may, therefore, be stated in this form : — Y—N-—-V R—N-—-B P—N—G Observe that the coniplementaries balance, one against the other, on the intermediate neutral  ... 

The Role of Musical Notes and Color Frequencies for Balancing Chakras in Human Body

Dr. Ankita Bhetiwal
2017 International Journal for Research in Applied Science and Engineering Technology  
Both the sound and color can be represented by the frequencies and can be used for balancing the chakras in human body.  ...  It is very important for the humans to keep these chakras balanced so as to keep their mind and body physically and emotionally healthy.  ...  Frequency in Hz * 2 ^40 . 3 that the color frequency interval is nothing but the frequency interval of the chakras and the frequencies that can be used to heal the chakras must fall in this interval  ... 
doi:10.22214/ijraset.2017.8221 fatcat:u2wl742ozvfttkl5e3raxy6ghm

Page 229 of SMPTE Motion Imaging Journal Vol. 77, Issue 3 [page]

1968 SMPTE Motion Imaging Journal  
The single-line color-bar pulses, after encoding, give on an oscilloscope, having a facility of vertical-interval intensifica- tion, a color-bar signal-waveform indica- tion of (1) the white-balance at  ...  It is seen that the con- ventional 8-interval color-bar signal is simplified to 6 intervals in this applica- tion.  ... 

Simplest Color Balance

Nicolas Limare, Jose-Luis Lisani, Jean-Michel Morel, Ana Belén Petro, Catalina Sbert
2011 Image Processing On Line  
There are many sophisticated algorithms in the literature performing color balance or other color contrast adjustments.  ...  By stretching the color scales, the image becomes brighter. If there was a colored ambient light, for example electric light where R and G dominate, the color balance will enhance the B channel.  ...  As we explained before, a potential problem with this approach is that two aberrant pixel colors reaching the color interval extrema are enough to inhibit any image transform by this naive color balance  ... 
doi:10.5201/ipol.2011.llmps-scb fatcat:n5ljhvo7bvaqtopf3asvczk2my

Efficient Splitting of Measures and Necklaces [article]

Noga Alon, Andrei Graur
2020 arXiv   pre-print
In the problem ϵ-CONSENSUS SPLITTING, there are n non-atomic probability measures on the interval [0, 1] and k agents.  ...  The goal is to divide the interval, via at most n (k-1) cuts, into pieces and distribute them to the k agents in an approximately equitable way, so that the discrepancy between the shares of any two agents  ...  Suppose the Balancer cuts the remainder of the necklace and allocates the resulting intervals R 1 , ..., R u to agent 1 and T 1 , ..., T v to agent 2 to obtain a balanced allocation.  ... 
arXiv:2006.16613v1 fatcat:zmjna7flnvez7nu5pdoovs2l3a

Parameterized Complexity in Multiple-Interval Graphs: Partition, Separation, Irredundancy [chapter]

Minghui Jiang, Yong Zhang
2011 Lecture Notes in Computer Science  
We present new results on the parameterized complexities of k-VERTEX CLIQUE PARTITION and k-SEPARATING VERTICES in multiple-interval graphs and their complements, and present a very simple alternative  ...  the graph is a balanced t-interval graph.  ...  CUTTING INTO l COMPONENTS in balanced 2-track interval graphs and co-balanced 3-track interval graphs is W[1]-hard with parameters k and l.  ... 
doi:10.1007/978-3-642-22685-4_6 fatcat:7r4kzz5htnebthuz45eyurujmu
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