Low Power Dynamic Scheduling for Computing Systems

This paper considers energy-aware control for a computing system with two states: "active" and "idle." In the active state, the controller chooses to perform a single task using one of multiple task processing modes. The controller then saves energy by choosing an amount of time for the system to be idle. These decisions affect processing time, energy expenditure, and an abstract attribute vector that can be used to model other criteria of interest (such as processing quality or distortion). The goal is to optimize time average system performance. Applications of this model include a smart phone that makes energy-efficient computation and transmission decisions, a computer that processes tasks subject to rate, quality, and power constraints, and a smart grid energy manager that allocates resources in reaction to a time varying energy price. The solution methodology of this paper uses the theory of optimization for renewal systems developed in our previous work. This paper is written in tutorial form and develops the main concepts of the theory using several detailed examples. It also highlights the relationship between online dynamic optimization and linear fractional programming. Finally, it provides exercises to help the reader learn the main concepts and apply them to their own optimizations. This paper is an arxiv technical report, and is a preliminary version of material that will appear as a book chapter in an upcoming book on green communications and networking.Comment: 26 pages, 10 figures, single spac

Finding the Median (Obliviously) with Bounded Space

We prove that any oblivious algorithm using space $S$ to find the median of a list of $n$ integers from $\{1,...,2n\}$ requires time $\Omega(n \log\log_S n)$. This bound also applies to the problem of determining whether the median is odd or even. It is nearly optimal since Chan, following Munro and Raman, has shown that there is a (randomized) selection algorithm using only $s$ registers, each of which can store an input value or $O(\log n)$-bit counter, that makes only $O(\log\log_s n)$ passes over the input. The bound also implies a size lower bound for read-once branching programs computing the low order bit of the median and implies the analog of $P \ne NP \cap coNP$ for length $o(n \log\log n)$ oblivious branching programs

Finite automata with advice tapes

We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.Comment: Corrected typo

Subsampling Algorithms for Semidefinite Programming

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls granularity, i.e. the tradeoff between cost per iteration and total number of iterations. Furthermore, the total computational cost is directly proportional to the complexity (i.e. rank) of the solution. We study numerical performance on some large-scale problems arising in statistical learning.Comment: Final version, to appear in Stochastic System