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In many applications such as IP network management, data arrives in streams, and queries over those streams need to be processed online using limited storage. Correlated-sum (CS) aggregates are a natural class of queries formed by composing basic aggregates on (x, y) pairs, and are of the form SUM{g(y) : x ≤ f (AGG(x))}, where AGG(x) can be any basic aggregate and f (), g() are user-specified functions. CSaggregates cannot be computed exactly in one pass through a data stream using limited storage; hence, we study the problem of computing approximate CS-aggregates.We guarantee a priori error bounds when AGG(x) can be computed in limited space (e.g., MIN, MAX, AVG), using two variants of Greenwald and Khanna's summary structure for the approximate computation of quantiles. Using real data sets, we experimentally demonstrate that an adaptation of the quantile summary structure uses much lesser space, and is significantly faster, than a more direct use of the quantile summary structure, for the same a posteriori error bounds. Finally, we prove that, when AGG(x) is a quantile (which cannot be computed over a data stream in limited space), the error of a CS-aggregate can be arbitrarily large.

Abstract-Dummy fills are being extensively used to enhance CMP planarity. However presence of these fills can have a significant impact on the values of interconnect capacitances. Accurate capacitance extraction accounting for these dummies is CPU intensive and cumbersome. For one, there are typically hundreds to thousands of dummy fills in a small layout region, which stress the general purpose capacitance extractor. Second, since these dummy fills are not introduced by the designers, it is of no interest for them to see the capacitances to dummy fills in the extraction reports; they are interested in equivalent capacitances associated with signal power and ground nets. Hence extracting equivalent capacitances across nets of interest in the presence of large number of dummy fills is an important and challenging problem. We present a novel extension to the widely popular MonteCarlo capacitance extraction technique. Our extension handles the dummy fills efficiently. We demonstrate the accuracy and scalability of our approach by two methods (i) classical and golden technique of finding equivalent interconnect capacitances by eliminating dummy fills through the network reduction method and (ii) comparing extracted capacitances with measurement data from a test chip.

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