Two-Dimensional Cutting Problem

This paper deals with two-dimensional cutting problems. Firstly the complexity of the problem in question is estimated. Then, several known approaches for the regular (rectangular) and irregular (not necessarily rectangular) cutting problems are described. In the second part, a decision support system for cutting a rectangular sheet of material into pieces of arbitrary shapes, is presented. The system uses two earlier described methods which prefer different types of data and the user may decide which one is more suitable for the problem in question. After brief description of system data files and its manual, some experimental results are presented

Sequencing by Hybridization of Long Targets

Sequencing by Hybridization (SBH) reconstructs an n-long target DNA sequence from its biochemically determined l-long subsequences. In the standard approach, the length of a uniformly random sequence that can be unambiguously reconstructed is limited to due to repetitive subsequences causing reconstruction degeneracies. We present a modified sequencing method that overcomes this limitation without the need for different types of biochemical assays and is robust to error

In vitro and in vivo studies on biocompatibility of carbon fibres

In the present study we focused on the in vitro and in vivo evaluation of two types of carbon fibres (CFs): hydroxyapatite modified carbon fibres and porous carbon fibres. Porous CFs used as scaffold for tissues regeneration could simultaneously serve as a support for drug delivery or biologically active agents which would stimulate the tissue growth; while addition of nanohydroxyapatite to CFs precursor can modify their biological properties (such as bioactivity) without subsequent surface modifications, making the process cost and time effective. Presented results indicated that fibre modification with HAp promoted formation of apatite on the fibre surface during incubation in simulated body fluid. The materials biocompatibility was determined by culturing human osteoblast-like cells of the line MG 63 in contact with both types of CFs. Both tested materials gave good support to adhesion and growth of bone-derived cells. Materials were implanted into the skeletal rat muscle and a comparative analysis of tissue reaction to the presence of the two types of CFs was done. Activities of marker metabolic enzymes: cytochrome c oxidase (CCO) and acid phosphatase were examined to estimate the effect of implants on the metabolic state of surrounding tissues. Presented results evidence the biocompatibility of porous CFs and activity that stimulates the growth of connective tissues. In case of CFs modified with hydroxyapatite the time of inflammatory reaction was shorter than in case of traditional CFs

Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2

In this paper we study variants of the non-preemptive parallel job scheduling problem in which the number of machines is polynomially bounded in the number of jobs. For this problem we show that a schedule with length at most (1 + ε)OPT can be calculated in polynomial time. Unless P = NP, this is the best possible result (in the sense of approximation ratio), since the problem is strongly NP-hard. For the case, where all jobs must be allotted to a subset of consecutive machines, a schedule with length at most (1.5 + ε)OPT can be calculated in polynomial time. The previously best known results are algorithms with absolute approximation ratio 2. Furthermore, we extend both algorithms to the case of malleable jobs with the same approximation ratios