In Digital Image Steganography, Pixel-Value Differencing (PVD) methods use the difference between neighboring pixel values to determine the amount of data bits to be inserted. The main advantage of these methods is the size of input data that an image can hold. However, the fall-off boundary problem and the fall in error problem are persistent in many PVD steganographic methods. This results in an incorrect output image. To fix these issues, usually the pixel values are either somehow adjusted or simply not considered to carry part of the input data. In this paper, we enhance the Tri-way Pixel-Value Differencing method by finding an optimal pixel value for each pixel pair such that it carries the maximum input data possible without ignoring any pair and without yielding incorrect pixel values.

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The Rural Postman Problem (RPP) is a classical arc routing problem proven to be NP-Hard whith applications in many contexts of practical interest. A common strategy for solving RPP instances is to first determine a suitable graph transformation in order to either reduce the dimensionality of the search space or to produce a single cursus graph to derive an Eulerian circuit in polynomial time. In this paper we present a simple but effective hybrid heuristic for the RPP that uses such a graph transformation and finds solutions using a Genetic Algorithm for global search and a local search algorithm to compute optimal traversal directions of a solution tour. Our approach is tested on a set of instances than have been already used in previously published work.