The standard measure for the quality of online algorithms is competitive ratio. This generally applicable, and some problems it works well, but others fails to distinguish between that have very different performance. Thus, ever since its introduction, researchers worked on improving measure, defining variants, or measures based other concepts improve situation. Relative worst-order analysis (R...

Introduction: The most common substance of abuse/dependence in patients presenting for treatment in western countries is alcohol. Ethyl alcohol or ethanol which is also called medicinal alcohol is used as an official drug compendium. It is also administered as an antidote in methanol poisoning. However, regular consumption of high amounts of alcoholic drinks induces dependence and addiction lea...

In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the eeectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.