Maximizing the Minimum Load for Selfisch Agents

We consider the problem of maximizing the minimum load for machines that are controlled by selfish agents, who are only interested in maximizing their own profit. Unlike the classical load balancing problem, this problem has not been considered for selfish agents until now. For a constant number of machines, $m$, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a new technique for reducing the number of jobs while remaining close to the optimal solution. We also present an FPTAS for the classical machine covering problem, i.e., where no selfish agents are involved (the previous best result for this case was a PTAS) and use this to give a monotone FPTAS. Additionally, we give a monotone approximation algorithm with approximation ratio $min(m,(2+eps)s_1/s_m)$ where $eps>0$ can be chosen arbitrarily small and $s_i$ is the (real) speed of machine $i$. Finally we give improved results for two machines

Algorithms for balancing demand-side load and micro-generation in Islanded Operation

Micro-generators are devices installed in houses pro-\ud ducing electricity at kilowatt level. These appliances can\ud increase energy efficiency significantly, especially when\ud their runtime is optimized. During power outages micro-\ud generators can supply critical systems and decrease dis-\ud comfort.\ud In this paper a model of the domestic electricity infras-\ud tructure of a house is derived and first versions of algo-\ud rithms for load/generation balancing during a power cut\ud are developed. In this context a microCHP device, produc-\ud ing heat and electricity at the same time with a high effi-\ud ciency, is used as micro-generator.\ud The model and the algorithms are incorporated in a sim-\ud ulator, which is used to study the effect of the algorithms for\ud load/generation balancing. The results show that with some\ud extra hardware all appliances in a house can be supplied,\ud however not always at the preferred time.\u