Energy-Efficient Broadcast Scheduling for Speed-Controlled Transmission Channels

We consider the problem of computing energy-efficient broadcast schedules for a speed-controlled broadcast channel, i.e., our goal is to find broadcast schedules that minimze overall energy consumption, where sending at speed s for t time units consumes energy t·sα and transmission speed for each broadcast needs to be fixed when it is started. The main part of the paper is focused on the case that the server holds only a single message and every request defines a strict deadline before which a full broadcast has to be performed. We present an O(2α)-competitive deterministic online algorithm and prove that this is asymptotically best possible even allowing randomization. We then discuss some possible problem extensions. For the case of multiple different messages we prove that an extension of our online algorithm achieves competitive ratio (4c− 1)α if the lengths of requests do not vary by more than a factor of c. For the problem variation in which the speed of running broadcasts may be changed, we present lower bounds showing that competitive ratios that depend exponentially on α are still unavoidable.