By Gelb A.

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**Additional resources for Applied optimal estimation**

**Example text**

The cost model that has been utilised in our work is presented in [87,89,90,91]. 1 Classification of Application Data in the Cloud In general, there are two types of data stored in the cloud storage À original data and generated data: 1. Original data are the data uploaded by users, and in scientific applications they are usually the raw data collected from the devices in the experiments. In the cloud, they are the initial input of the applications for processing and analysis. The most important feature of these data is that if they are deleted, they cannot be regenerated by the system.

For example, e , di, dj . 5 is an out-block edge of block B1, and also an in-block edge of block B2. In the algorithm, if edge e , di, dj . ) from the current CTT, since e , di, dj . is an in-block edge of block B2. ), for example e , dh, dk . 5, we need to find the MCSS of the sub-branch fd1 ; d2 ; . ; d 0m g of block B2. However, because e , di, dj . is also an out-block edge of B1, di is not the only data set in provSet of d10 . To calculate the generation cost of d1, we need to find its stored provenance data sets from sub-branch Br1 of block B1.

This equation guarantees that the length of the SP with an out-block edge or overblock edge still equals the minimum cost rate of the data sets, which is: 0 Pmin , ds ; dj . dj g 1 CostRk A S0 Hence to calculate the weights of out-block and over-block edges, we have to find the MCSS of the data sets that are in the sub-branches of the block. For example, the weight of the edge e , d5, d8 . 3 is: ω , d5 ; d8 . 5 y8 1 genCostðd6 Þ Ã v6 1 genCostðd7 Þ Ã v7 1 ðCostR3 1CostR4 ÞS0 where we have to find the MCSS of data sets d3 and d4.