Aggregate (or aggr for short) queries, in particular SUM queries, are crucial for many applications that need to deal with uncertain data . Let us give two motivating examples from the medical and environmental domains. Effect of the number of uncertain tuples using the synthetic data, the response time of the three algorithms vs. the number of uncertain tuples, i.e. n, and the other experimental parameters set as described. The best algorithm is DP_PSUM, and the worst is the Naive algorithm. For n>30, the response time of the Naive algorithm is too long, such that we had to halt it. This is why we do not show its response time for n>30. The response time of DP_PSUM is at least four times lower than that of Q_PSUM (notice that the figure is in logarithmic scale). Over the IIP database, the response time of the three algorithms, with different samples of the IIP database. In each sample, we picked a set of n tuples, from the first to the nth tuple of the database. Overall, the results are qualitatively in accordance with those over synthetic data. The response time over the real database is higher than that of the synthetic database. The main reason is that the precision of the real data , i.e. there is one digit after the decimal point. This increases the execution time of our algorithms significantly. The case of DP_PSUM, the execution time can increase up to ten times, and this confirms the complexity analysis of real value processing. Effect of data distribution the response time of our algorithms over the Uniform and Gaussian databases. The response time of DP_PSUM over uniform distribution increases, but not significantly, i.e. less than 30%. The higher performance of DP_PSUM over the uniform distribution is due to the higher number of zero points, which can be skipped, thus less computation is needed. Another reason is the value of MaxSum, i.e. the maximum possible sum value, which is lower for the uniform dataset.

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