Odd Harmonious Labeling of Some Graphs

The labeling of discrete structures is a potential area of research due to its wide range of applications. The present work is focused on one such labeling called odd harmonious labeling

The economics of GM food labels: An evaluation of mandatory labeling proposals in India

"Labeling of genetically modified (GM) foods is a contentious issue and internationally, there is sharp division whether such labeling ought to be mandatory. This debate has reached India where the government has proposed mandatory labeling. In this context, this paper evaluates the optimal regulatory approach to GM food labels. Mandatory labeling aims to provide greater information and correspondingly more informed consumer choice. However, even without such laws, markets have incentives to supply labeling. So can mandatory labeling achieve outcomes different from voluntary labeling? The paper shows that this is not the case in most situations. The paper goes on to explore the special set of circumstances, where mandatory labeling makes a difference to outcomes. If these outcomes are intended, mandatory labeling is justified; otherwise not." from Authors' AbstractBiotechnology Economic aspects, Genetically modified food Developing countries, Biosafety, Food labeling,

Parsimonious Labeling

We propose a new family of discrete energy minimization problems, which we call parsimonious labeling. Specifically, our energy functional consists of unary potentials and high-order clique potentials. While the unary potentials are arbitrary, the clique potentials are proportional to the {\em diversity} of set of the unique labels assigned to the clique. Intuitively, our energy functional encourages the labeling to be parsimonious, that is, use as few labels as possible. This in turn allows us to capture useful cues for important computer vision applications such as stereo correspondence and image denoising. Furthermore, we propose an efficient graph-cuts based algorithm for the parsimonious labeling problem that provides strong theoretical guarantees on the quality of the solution. Our algorithm consists of three steps. First, we approximate a given diversity using a mixture of a novel hierarchical $P^n$ Potts model. Second, we use a divide-and-conquer approach for each mixture component, where each subproblem is solved using an effficient $\alpha$-expansion algorithm. This provides us with a small number of putative labelings, one for each mixture component. Third, we choose the best putative labeling in terms of the energy value. Using both sythetic and standard real datasets, we show that our algorithm significantly outperforms other graph-cuts based approaches

Sublinear Distance Labeling

A distance labeling scheme labels the $n$ nodes of a graph with binary strings such that, given the labels of any two nodes, one can determine the distance in the graph between the two nodes by looking only at the labels. A $D$-preserving distance labeling scheme only returns precise distances between pairs of nodes that are at distance at least $D$ from each other. In this paper we consider distance labeling schemes for the classical case of unweighted graphs with both directed and undirected edges. We present a $O(\frac{n}{D}\log^2 D)$ bit $D$-preserving distance labeling scheme, improving the previous bound by Bollob\'as et. al. [SIAM J. Discrete Math. 2005]. We also give an almost matching lower bound of $\Omega(\frac{n}{D})$. With our $D$-preserving distance labeling scheme as a building block, we additionally achieve the following results: 1. We present the first distance labeling scheme of size $o(n)$ for sparse graphs (and hence bounded degree graphs). This addresses an open problem by Gavoille et. al. [J. Algo. 2004], hereby separating the complexity from distance labeling in general graphs which require $\Omega(n)$ bits, Moon [Proc. of Glasgow Math. Association 1965]. 2. For approximate $r$-additive labeling schemes, that return distances within an additive error of $r$ we show a scheme of size $O\left ( \frac{n}{r} \cdot\frac{\operatorname{polylog} (r\log n)}{\log n} \right )$ for $r \ge 2$. This improves on the current best bound of $O\left(\frac{n}{r}\right)$ by Alstrup et. al. [SODA 2016] for sub-polynomial $r$, and is a generalization of a result by Gawrychowski et al. [arXiv preprint 2015] who showed this for $r=2$.Comment: A preliminary version of this paper appeared at ESA'1

Nutrition Labeling in the United States and the Role of Consumer Processing, Message Structure, and Moderating Conditions

It has been since 1990 that the landmark Nutritional Labeling Education Act (NLEA) was passed in the United States, and since 1969 that the first White House Conference on Food, Nutrition and Health occurred. In the time since these important events, considerable research has been conducted on how U.S. consumers process and use nutritional labeling. An up-to-date review of nutritional labeling research must address key findings on the processing and use of nutrition facts panels (NFPs), restaurant labeling, front-of-pack (FOP) symbols, health and nutrient content claims, new labeling efforts (e.g., for meat products), and claims not regulated by the U.S. Food and Drug Administration (FDA). Message structure mediates the ways in which consumers process nutritional labeling while moderating conditions affect research outcomes associated with labeling efforts. The most recent policy issues and problems to be considered (e.g., by the FDA) include nutritional labeling as well as identifying opportunities for consumer research in helping to promote healthy lifestyles and reducing obesity in the United States and throughout the world. For example, several unanswered research questions remain regarding how the proposed changes to the NFPs—beef, poultry, and seafood labeling; restaurant chain calorie labeling; alternative FOP formats; and regulated and unregulated health and nutrient content claims—will affect consumers. Researchers have yet to examine not only these different labeling and nutrition information formats, but also how they might interact with one another and the role of key moderating conditions (e.g., one’s motivation, ability opportunity to process nutrition information) in affecting consumer processing and behavior

1-Relaxed Edge-Sum Labeling Game

We introduce a new graph labeling and derive a game on graphs called the 1-relaxed modular edge-sum labeling game. Given a graph G and a natural number n, we define a labeling by assigning to each edge a number from {1,..., n} and assign a corresponding label for each vertex u by the sum of the labels of the edges incident to u, computing this sum modulo n. Similar to the chromatic number, we define L(G) for a graph G as the smallest n such that G has a proper labeling. We provide bounds for L(G) for various classes of graphs. Motivated by competitive graph coloring, we define a game on using modular edge-sum labeling and determine the chromatic game number for various classes of graphs. We will emphasize some characteristics that distinguish this labeling from traditional vertex coloring