The existing literature gives efficient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general plane graphs. Our results show two algorithms for mapping four-connected plane graphs with at mo...

Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. In fact, the behavior of real-world networks and random graph models can be the complete opposite of one another, depending on the considered property. Brach, Cygan, Lacki, and Sankowski [SODA 2...

Inhomogeneous random graphs are commonly used models for complex networks where nodes have varying degrees of connectivity. Computing the degree distribution such is a fundamental problem and has important applications in various fields. We define inhomogeneous graph as model edges drawn independently probability link between any two vertices can be different each node pair. In this paper, we p...

The lognormal distribution had long been thought to be the most appropriate probability distribution for Japanese sentence length distributions. Yet this view had been supported only by few researches with sparse sampling data and reasoning contradicting language reality. In order to show a more realistic approach, we analyzed a substantial number of samples. At first, 150 essays and short stor...

The existing literature gives efficient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general plane graphs. Our results show two algorithms for mapping four-connected plane graphs with at mo...

Today, methods for marking parts and components in industrial production are constantly improving, they must meet several basic criteria active traceability by consumers. The parameter that is of paramount importance the quality related to contrast marked sign or QR code. To achieve optimal contrast, a number technological factors functional relationships between them be taken into account.The ...