A PTAS for a resource scheduling problem with arbitrary number of parallel machines

In this paper we study a parallel machine scheduling problem with non-renewable resource constraints. That is, besides the jobs and machines, there is a common non-renewable resource consumed by the jobs, which has an initial stock and some additional supplies over time. Unlike in most previous results, the number of machines is part of the input. We describe a polynomial time approximation scheme for minimizing the makespan

Epiphytic diatoms of the Tisza River, Kisköre reservoir and some oxbows of the Tisza River after the cyanide and heavy metal pollution in 2000

The Tisza River is a large tributary of the Danube River. The largest reservoir of the river is the Kisköre reservoir, and there are furthermore a great number of oxbows in the vicinity of the river. In February and early spring 2000 serious amounts of cyanide and heavy metal pollution were spilled into the Tisza River. The Kisköre Reservoir of the Tisza was less polluted than the river itself. However, the four oxbows investigated were flooded by the Tisza River in April 2000. Epiphytic diatom samples were taken in February and October 2000 along the Tisza River, in November and December 2000 at the Kisköre Reservoir and in May and July 1996, October 2000 and June 2001 at the four Tisza oxbows. The aims of this study were to obtain preliminary data about the species composition of the attached diatoms of these waters, to evaluate the impact of the pollution on epiphytic diatoms and to evaluate the natural protection value of these waters. Epiphyton of the Tisza River was dominated by Achnanthidium minutissimum, Amphora pediculus, Cocconeis placentula, Diatoma moniliformis in February and by Achnanthidium minutissimum and several Nitzschia spp. in October. A number of teratological frustules were observed. In the Kisköre reservoir, Amphora pediculus, Cocconeis pediculus, C. placentula, Cyclotella meneghiniana, Gomphonema angustum, Nitzschia dissipata were dominant. In 1996 Staurosira, Staurosirella and Navicula species dominated in the oxbows, whereas in 2000 Aulacoseira distans, Achanthidium minutissimum and Nitzschia spp. became dominant. Based on results from the literature, we are of the opinion that the characteristic Achnanthidium minutissimum - Nitzschia spp. dominance of the Tisza River and the oxbows is partly due to the heavy metal pollution. A number of endangered species, two new elements for the Hungarian diatom flora - Navicula austrocollegarum and Navicula streckerae - and two probably invasive species, Diadesmis confervacea and Didymosphenia geminata were found