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We consider the problem of tracking with small relative error an integer function <i>f</i>(<i>n</i>) defined by a distributed update stream <i>f</i>'(<i>n</i>) in the distributed monitoring model. In this model, there are <i>k</i> sites over which the updates <i>f</i>'(<i>n</i>) are distributed, and they must communicate with a central coordinator to… (More)

A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O(1 ε log 1 ε) words of memory. This improves upon the previous best upper bound… (More)

A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O(1 ε log 1 ε) words of memory. This improves upon the previous best upper bound… (More)

We consider the problem of scheduling a set of n tasks on m processors under precedence, communication , and global system energy constraints to minimize makespan. We extend existing scheduling models to account for energy usage and give convex programming algorithms that yield essentially the same results as existing algorithms that do not consider energy,… (More)

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