LONDON - Oil prices rebounded on Tuesday, as a weaker dollar boosted demand and in the wake of upbeat German economic data, analysts said. Brent North Sea crude for delivery in March gained 65 cents to $112.36 a barrel in London midday deals. New York's main contract, light sweet crude for February, edged up six cents to $95.62 a barrel. Crude prices had fallen on Monday as investors banked profits following gains last week driven by encouraging economic data from the United States and China, and the hostage killings in oil and gas producer Algeria, traders said.