We show that a context-free grammar of size produces single string $w$?> length $n$?> (such is also called straight-line program) can be transformed in linear time into for $\mathcal {O}(m)$?> , whose unique derivation tree has depth {O}(\log n)$?> . This solves an open problem the area grammar-based compression, improves many results this area, and greatly simplifies existing const...

A practical application of the spherical involute surface to the forged straight bevel gears is provided and demonstrated in this work. Conjugate (pure involute) theoretical surfaces are developed from the input design parameters. The surfaces are modified to suit the actual application (automotive differential). The unloaded (or low load) tooth contact analysis of modified surfaces is performe...

We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with ...

This paper proposes a simplified approach to the assembly of large physical genome maps. The approach focuses on two key problems: (i) the integration of diverse forms of data from numerous sources, and (ii) the detection and removal of errors and anomalies in the data. The approach simplifies map assembly by dividing it into three phases-overlap, linkage and ordering. In the first phase, all f...