Ever since the world war, the call for information security raised. The explosion in World Trade Centre alarmed the people to work more towards secured travel of data. Then Steganography came to rescue, as here communication is also obscured. In many of the applications size of the secret data will be less than that of the size of the Cover Image which results in wastage of bandwidth. In this proposed study, multi-user embedding is carried out and is implemented for 5 users. A graceful graph is used for fixing the randomized order of embedding.

Priority in the order of embedding among the five users will be changed during every cycle. The hackers also grew up to counter these safety measures. Rupert Murdoch, Julian Assange to name a few. Hence, Emphasis given on a powerful algorithm.

Conventional steganography involves the concept of one image per user, where only one user can embed the information within an image. The proposed work here has gone up a level where up to five users can use a single colour image to embed and transmit their data. Each user has been assigned a pixel to embed ones data and after embedding, one has to go to other pixel for embedding which will be determined by the Graceful Labeling methodology and the order of user index will be all combinations of five users i.

This introduces the randomization in the order of embedding. Randomization in the selection of planes is done by using a slightly altered PIT. This Randomized multi-user steganography amplify the strength of the system and thus making attack nohow.

A decade back, Information technology was just a branch of study. In the world of internet, people have reached such great heights that anything is just but surely possible. The communication sector taking IT and its developments as a platform has also made renovations in itself. This all innovations exhibit major platform is the Internet and again the base being the Information technology. With so many advantages of IT, there are again equivalent or rather more number of disadvantages and one of the major being security.This paper takes a close look at graceful labelling and its applications.

Finally, we show how spectral graph theory can be used to further the progress on the Graceful Tree Conjecture. This is a preview of subscription content, log in to check access. Abrham J. Adamaszek, M. Aldred R. Alfalayleh, M. Arkut, I. In: Proc. SPIE, vol. OptiComm Optical Networking and Communications. Imrich Chlamtac; Ed Baca M. Ars Comb.

### BPDR: A New Dimensionality Reduction Technique

Bermond, J. In: Graph Theory and Combinatorics. Pitman, London, pp. Bermond J. Bhat-Nayak V. Indian Acad. Bloom G. IEEE 65— Bloom, G.

Springer-Verlag, New York In: Alavi, Y.

**Stanford Lecture: Donald Knuth - "Trees and chordal graphs" (2012)**

Graph Theory with Applications to Algorithms and Computers. Wiley, New York Bonnington C. Graph Theory 3137—56 Brankovic, L. Brankovic L. Cavenagh N. Chen W.Label the vertices of a simple undirected graph where and with integers from to. Now label each edge with absolute difference of the labels of its incident vertices. The labeling is said to be graceful if the edges are labelled through inclusive with no number repeated.

A graph is called graceful if it has at least one such labeling. This labeling was originally introduced in by Rosa. The name graceful labeling was coined later by Golomb.

Gracefully labeled graphs serve as models in a wide range of applications including coding theory and communication network addressing. The graceful labeling problem is to determine which graphs are graceful. It is conjectured by Kotzig, Ringel and Rosa that all trees are graceful. Despite numerous more than publications on graceful labeling for over three decades, only a very restricted classes of trees and also of some other graphs have been shown to be graceful.

These restricted classes include paths, stars, complete bipartite graphs, prism graphs, wheel graphs, caterpillar graphs, olive trees, and symmetrical trees. Good luck. I'm surprised to see such a short proof for such a long-standing open problem, but surely people who are a lot more into the subject than I will be able to provide more constructive comments on the paper.

It's a bit worrisome that this is already the eight version on the arXiv I haven't read the paper though Truly, this was unfortunate choice of wording; I corrected it.

Btw to provide a graceful labeling for complete bipartite graphs is quite an easy exercise. Open Problem Garden.

### Graceful Labeling of Assignable Information Hiding in Image

Help About Contact. Keywords: combinatorics graceful labeling. Posted by: kintali on: July 13th, Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv. Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Redl Published Mathematics. Given a graph consisting of vertices and edges, a vertex labeling of is an assignment of labels to the vertices of that produces for each edge a label depending on the vertex labels and.

A vertex labeling is called a graceful labeling of a graph with edges if is an injection from the vertices of to the set 0, 1. A graph is called graceful if there exists a graceful labeling of see Fig.

View PDF. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Figures and Tables from this paper. Figures and Tables. Citations Publications citing this paper.

Gallian Mathematics Applications of mathematical programming in graceful labeling of graphs Kourosh EshghiParham Azimi Mathematics On the embedding of cone graphs in the line with distinct distances between neighbors Rodrigo M. ZhouCelina M. References Publications referenced by this paper.Algorithms for optimization problems typically go through a sequence of steps, with a set of choices at each step. For many optimization problems, using dynamic programming to determine the best choices is overkill; simpler, more efficient algorithms will do.

A greedy algorithm always makes the choice that looks best at the moment. That is, it makes a locally optimal choice in the hope that this choice will lead to a globally optimal solution. This chapter explores optimization problems that are solvable by greedy algorithms. Greedy algorithms do not always yield optimal solutions, but for many problems they do. We shall first examine in Section Next, Section Section In Section Finally, Section The greedy method is quite powerful and works well for a wide range of problems.

Minimum spanning trees form a classic example of the greedy method. Although this chapter and Chapter 24 can be read independently of each other, you may find it useful to read them together.

We shall find that a greedy algorithm provides an elegant and simple method for selecting a maximum-size set of mutually compatible activities. The activity-selection problem is to select a maximum-size set of mutually compatible activities. A greedy algorithm for the activity-selection problem is given in the following pseudocode.

The set A collects the selected activities. The variable j specifies the most recent addition to A. Since the activities are considered in order of nondecreasing finishing time, f j is always the maximum finishing time of any activity in A.Telegram Me. Have you ever experienced that moment where you insert your 16GB memory card into the camera only to discover that this new, freshly formatted card is a nickel short of 15GB?

Or a 32GB card turning to Have you ever wondered where those GigaBytes are hiding? The truth is that they are not hiding at all. It has to do more with the way card companies and hard drive companies too decide to annotate their products. This system is called the SI units system. This is called the Binary units system. For Kilo, the difference is only 2. Memory cards manufactures choose to use the SI system to denote cards sizes. Our computers and card readers use the binary system for size calculation and here is where the missing Bytes are.

Of course, the card companies are covered, they do mention this fact on their sites in a small asterisk, or with hover text that is revealed when you hover over a small asterisk. Here are screen shots from three leading cards and hard drive manufacturers, though they are not the only one to use that practice:. If you followed the math, you probably realized that the toll this calculation method in taking gets bigger the bigger the data units are.

So while the toll on a 1GB memory card in way smaller than on a 1 tera hard drive. Have a look at this table to sum things up:.

Now What? Now, I think it would be fair if we politely asked memory card makes and hard drive makers to switch to binary so they will be better aligned with the way we use them. Udi Tirosh is the Founder and Editor in Chief of DIYPhotography, he is also a photographer, a relentless entrepreneur, a prolific inventor and a dad, not necessarily in that order. For the Record, this has been the way all storage capacity including Floppy and Hard Drives are denoted.

Since then media companies had to put the asterisk. I find it funny that eventhough they follow the binary methodology, they were still making cards using the SI numbering system, Go back and change history. There is no conspiracy or lies here. The generally accepted reason is both were initially developed prior to overwhelming use of binary. The HDD was introduced in and both binary and decimal formats were used. An example is the IBM which used decimal units for data and addressing.

Adding confusion to uncertainty in storage is that no storage device will ever hold as much data as printed on the label. Different file formats hold hidden data EXT Linux and NTFS Windows have hidden meta data associated with every file, users usually encounter this difference when dealing with file permissions.

All File systems reserve space for address look-up tables and the addresses themselves. Storage blocks were generally byte logical blocks but most modern large drives are now partitioned at byte blocks to keep address tables lookups performance reasonable to the larger files sizes.Dimensionality reduction algorithms such as LDA, PCA, or t-SNE are great tools to analyze unlabeled or labeled data and gain more information about its structure and patterns. Dimensionality Reduction gives us the ability to visualize high-dimension datasets which can be extremely helpful for model selection.

I believe that this subset of Machine Learning — call it data exploration — is wildly underdeveloped compared to its counterparts like supervised learning or deep learning. My view: If someone is starting a new machine learning project, the first thing they do will be an exploratory analysis of the data.

Different researchers have their own ideas about how in-depth this step should be, however, the results of the data exploration is knowledge gained about the dataset at hand.

## Donate to arXiv

This knowledge proves to be extremely valuable down the road when the researcher runs into various problems like model selection and hyper-parameter tuning.

By starting at the root and developing beautiful data exploration algorithms that will give the user quality information about the underlying patterns of a dataset, we can thus develop better machine learning pipelines as a whole.

The idea is bit-packing: encoding various data points into one — long — binary string. I will spare many of the nitty-gritty details on how the algorithm is constructed. A general overview of the algorithm is the following: The original data columns which all must be numerical are first ranked by importance. The data is then normalized to be centered around 0. The normalized data is binary packed into the bit strings in the order of their feature importance.

Finally, we are left with packed binary numbers that can be converted back to integers. For a 4 column dataset that will be reduced to 2 columns, the binary packing looks like this:. Once again, this section is made as a general overview on how the algorithm works, however, it is not very in depth. I structured the BPDR module such that it mimics how other dimensionality algorithms work in the Scikit-Learn package.

Here is an example of its use on the iris dataset. After navigating to the BPDR directory, run pip install -r requirements. Now we are finally ready to open a new file and begin exploring data. First, we must import the required packages into our module: We will be obviously using BPDR, as well as the all-to-popular iris dataset, and matplotlib for some visualization:.

Next, we load our dataset:. We see that there are 4 columns all numerical.

Let us reduce this dataset to 2 columns so that we can graph and visualize the reduced components. We first need to create an instance of the reduction object and initialize its parameters.

Since we passed in labels, we can look at some variance metrics that evaluate how well the reduced data explains the original data:. For more information on how these variances are calculated please visit the documentation for the repository. Finally, we now have a dataset that is 2 columns wide which can be graphed and visualized.

When component 1 is graphed on the X-axis and component 2 is graphed on the Y-axis, the graph looks like this:.

## Comments