| This dissertation looks at various online problems such as task scheduling, packet scheduling, and k-server, using energy as an optimization criterion. In the task scheduling problem, we attempt to schedule tasks on a single variable-speed processor. Our work differs from previous results in two major ways. First, we consider a model where not all tasks need to be completed, and where the goal is to maximize the difference between the benefit of completed tasks and the cost of energy (previous work assumed that all tasks must be completed). Second, we permit a wide range of functions relating task completion time to energy (previous work assumed a polynomial relationship).;We will also explore a novel online packet scheduling model related to energy-efficiency in mobile data transport. This model incorporates multiple networks with non-persistent connectivities where we only know which networks are available in the current timestep. When a packet arrives, it specifies a deadline and, for each network, a value it is worth if sent over that network. Our goal is to maximize the total value of packets we send by their deadlines. We demonstrate low-constant-competitive algorithms for this problem and several restrictions. We also provide lower bounds which closely match our competitive ratios and, under some restrictions, are tight.;Lastly, we will give the first polylog randomized online algorithm for k-server on hierarchically structured binary trees. In this problem, we are given a set of k initial server locations in some underlying metric space. Requests for service arrive at various nodes in this space, and as each request arrives we must move one of our k servers to that location, which requires a certain amount of energy. Our result makes substantial progress towards the goal of a polylog-competitive randomized algorithm for k-server on general metrics. |
