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### The Approximability of the Binary Paintshop Problem [chapter]

Anupam Gupta, Satyen Kale, Viswanath Nagarajan, Rishi Saket, Baruch Schieber
2013 Lecture Notes in Computer Science
By derandomizing this reduction for hard instances of the Min Uncut problem arising from the Unique Games Conjecture, we show that the Binary Paintshop problem is ω(1)-hard to approximate (assuming the  ...  In the Binary Paintshop problem, there are m cars appearing in a sequence of length 2m, with each car occurring twice. Each car needs to be colored with two colors.  ...  A ρ-approximation algorithm for Min Uncut can be used to give a ρ-approximation for the (generalized) Binary Paintshop problem. Using the algorithm of Agarwal et al.  ...

### Paintshop, odd cycles and necklace splitting

Frédéric Meunier, András Sebő
2009 Discrete Applied Mathematics
More generally, the "paint shop scheduling problem" is defined with an arbitrary multiset of colors given for each car, where this multiset has the same size as the number of occurrences of the car; the  ...  For the general problem concerning an arbitrary number of colors, we realize that the two aforementioned conjectures are corollaries of the celebrated "necklace splitting" theorem of Alon, Goldberg and  ...  The second author's research was partially supported by the Marie Curie network ''ADONET'' of the European Community.  ...

### Greedy colorings for the binary paintshop problem

Hadis Amini, Frédéric Meunier, Héloïse Michel, Atefeh Mohajeri
2010 Journal of Discrete Algorithms
This problem is denoted by PPW(2, 1).  ...  Moreover, we show that when one draws uniformly at random an instance w of PPW(2, 1), the greedy algorithm needs at most 1/3 of the length of w color changes.  ...  We call this problem the binary paintshop problem. If cars are considered to be letters in an alphabet, the following is a formalization. PPW(2, 1) (Binary Paint Shop Problem).  ...

### Computing solutions of the paintshop–necklace problem

Frédéric Meunier, Bertrand Neveu
2012 Computers & Operations Research
The first problem is the paint shop problem, defined by Epping, Hochstättler and Oertel in 2004.  ...  The main purpose of the present paper is to make a step in a more operational direction for these two problems by discussing practical ways to compute solutions for instances of various sizes.  ...  Introduction The paintshop-necklace problem.  ...

### An Optimal Lower Bound for Monotonicity Testing over Hypergrids [chapter]

2013 Lecture Notes in Computer Science
Approximability of the Binary Paintshop Problem Anupam Gupta, Satyen Kale, Viswanath Nagarajan, Rishi Saket and Baruch Schieber On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems  ...  total perimeter of homothetic convex bodies in a convex container Adrian Dumitrescu and Csaba Toth A pseudo-approximation for the genus of Hamiltonian graphs Yury Makarychev, Amir Nayyeri and Anastasios  ...

### PaintSHOP enables the interactive design of transcriptome- and genome-scale oligonucleotide FISH experiments [article]

Elliot A Hershberg, Jennie L Close, Conor K Camplisson, Sahar Attar, Ryan Chern, Yuzhen Liu, Shreeram Akilesh, Philip R Nicovich, Brian J Beliveau
2020 bioRxiv   pre-print
The goal of this freely available web resource is to democratize and standardize the process of designing complex probe sets for the oligo FISH community. PaintSHOP can be accessed at: paintshop.io  ...  Here, we introduce Paint Server and Homology Optimization Pipeline (PaintSHOP), an interactive platform for the reproducible design of oligo FISH experiments.  ...  Acknowledgements The authors thank G. Nir, D. Shechner, A. Tsue, H. Nguyen, J.Y. Kishi, and J. Harke for helpful feedback during the beta testing phase of PaintSHOP, N.  ...

### The Assessment of Car Making Plants with an Integrated Stochastic Frontier Analysis Model

Seog-Chan Oh, Jaemin Shin
2021 Mathematics
However, owing to the problem of multicollinearity, the general form of SFA is difficult to apply to the assessment of complex manufacturing systems in the automotive industry, which is characterized by  ...  For illustration of the proposed approach, hypothetical vehicle assembly plants are assessed as examples, where the total labor hours are split into Bodyshop, Paintshop, and General Assembly, exclusively  ...  quality problems.  ...

### Some heuristics for the binary paint shop problem and their expected number of colour changes

Stephan Dominique Andres, Winfried Hochstättler
2011 Journal of Discrete Algorithms
In the binary paint shop problem we are given a word on n characters of length 2n where every character occurs exactly twice.  ...  The objective is to colour the letters of the word in two colours, such that each character receives both colours and the number of colour changes of consecutive letters is minimized.  ...  Therefore the upper bound seems to be best possible. Another open question, which may be hard, is the following. Problem 17. What is the expected value of optimal colouring?  ...

### Gray-Level Reduction Using Local Spatial Features

Nikos Papamarkos, Antonios Atsalakis
2000 Computer Vision and Image Understanding
After training, the neurons of the output competition layer of the SOFM define the gray-level classes.  ...  This paper proposes a new method for reduction of the number of gray-levels in an image.  ...  According to the above analysis, the gray-scale reduction problem can be considered the problem of best transforming the original gray-level image to a new one with only J gray-levels as the final image  ...

### CONTROL OF LOW-RESOLUTION SCANNING OF OVARIAN TUMOR STROMAL COMPARTMENT

Nicolas Elie, Alexandre Labiche, Jean-Jacques Michels, Paulette Herlin
2011 Image Analysis and Stereology
To solve the problems linked to tumor heterogeneity and, hence, of quantization at the microscopic level, we developed an image-analysis strategy dedicated to estimating the proportion of tumor connective  ...  We performed a quality control in order to evaluate the efficiency of the proposed method of analysis at the selected resolution.  ...  The authors would like to thank any person who has contributed to this work and particularly Yves Denoux and Catherine Moricet.  ...

### A block encryption algorithm based on exponentiation transform

Nursulu Kapalova, Ardabek Khompysh, Müslüm Arici, Kunbolat Algazy, Duc Pham
2020 Cogent Engineering
The paper provides for statistical properties of the ciphertext obtained with the developed algorithm. We also present the results of differential and linear cryptanalysis of the S-box used.  ...  It describes a new transformation method EM (Exponentiation Module), which is part of the algorithm, and a method of S-box obtaining.  ...  Acknowledgements The research work was carried out within the framework of the project BR05236757 "Development of software and firmware means for cryptographic protection of information during its transfer  ...

### An Original Approach for Quantification of Blood Vessels on the Whole Tumour Section

Nga Tran Kim, Nicolas Elie, Benoît Plancoulaine, Paulette Herlin, Michel Coster
2003 Analytical Cellular Pathology
Relative abundance of tumour angiogenesis has been shown to be of clinical relevance in cancers of various locations such as the ovary.  ...  The slide scanner offers the advantage of recording an image of the whole histological section for subsequent automatic blood vessel detection and hot spot area location.  ...  Acknowledgements This work was supported by grants from the "Comités départementaux de la Ligue contre le Cancer de la Manche et du Calvados". Miss Tran is a fellow of the first committee.  ...

### WEAK PATTERN MATCHING IN COLORED GRAPHS: MINIMIZING THE NUMBER OF CONNECTED COMPONENTS

RICCARDO DONDI, GUILLAUME FERTIN, STÉPHANE VIALETTE
2007 Theoretical Computer Science
Furthermore, we prove the Min-CC problem for trees not to be approximable within ratio c log n for some constant c > 0, where n is the order of the target graph, and to be W[2]-hard when parameterized  ...  We consider in this paper the above-mentioned problem in one of its natural optimization forms, referred hereafter as the Min-CC problem: Find an occurrence of a motif in a vertexcolored graph, called  ...  Since |S 2 | = O Paintshop-For-Words problem 2,3,15 .  ...

### Combining low-frequency and spread-spectrum watermarking

Jessica Fridrich, Mark S. Schmalz
1998 Mathematics of Data/Image Coding, Compression, and Encryption
The image is first normalized and the watermark is embedded into the lowest frequency discrete cosine modes by encoding a binary pattern (a watermark) using a special quantization-like function.  ...  The low-frequency watermark is combined with a spread spectrum signal added to the middle frequencies of a DCT.  ...  The message of M symbols is then represented as spectrum signal S p is approximately Gaussian with zero mean and unit standard deviation even for moderate values of M (e.g., M ≈10).  ...

### An Analysis of Image Forgery Detection Techniques

Chandan Deep Kaur, Navdeep Kanwal
2019 Statistics, Optimization and Information Computing
It provides the comparative tables of various types of techniques to detect image forgery. It also gives an overview of different datasets used in various approaches of forgery detection.  ...  Images have the potential of conveying much more information as compared to the textual content. We pretty much believe everything that we see.  ...  But the problem with this approach is that it detects false result also.  ...
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