We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a r...

This paper presents an algorithm for the unconstrained two-dimensional cutting problem of rectangular pieces. It proposes the two-stage general block pattern that can be cut into general blocks in two stages, with another two or more stages being required to cut the blocks into pieces. Firstly vertical cuts divide the stock sheet into segments, and then horizontal cuts divide the segments into ...

Certain failing enlarged ischemic hearts are difficult to treat by mammary implants, epicardiectomy, omental grafts. A new concept and operation has been experimentally tested, based upon the omental graft’s ability to form arteriolar communications with surrounding arteries within eight days. in animals, three coronary arteries were surrounded by ameroid constrictors. Three separate omental st...

Based on the test results, a section of working bodies was selected for strip tillage, theheight, length soil disks were determined experimentally. As well as result acceptable tillage is combination bodies, consisting one cutting paws with soilproviding high rates crumbling quality cleansing them stubble and roots.

We propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as Mixed Integer Linear Programs (MIP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a...

Early regeneration success of upland oaks (Quercus spp. L.) was compared for three regeneration cutting treatments in the Sandstone Mountain Region of northern Alabama. Two 4-acre replications each of block dearcutting. strip cutting, and deferment cutting were established on north-facing slopes. The three harvesting treatments were applied in midsummer. Regeneration subplots were reinventoried...

Research addressing two-dimensional irregular shape packing has largely focused on the strip packing variant of the problem. However, it can be argued that this is a simplification. Materials from which pieces are required to be cut will ultimately have a fixed length either due to the physical dimensions of the material or through constraints on the cutting machinery. Hence, in order to cut al...