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Nowadays almost every major company has a monitoring system and produces log data to analyse their systems. To perform analysation on the log data and to extract experience for future decisions it is important to transform and synchronize different time series. For synchronizing multiple time series several methods are provided so that they are leading to a synchronized uniform time series. This is achieved by using discretisation and approximation methodics. Furthermore the discretisation through ticks is demonstrated, as well as the respectivly illustrated results.
In this note we look at anisotropic approximation of smooth functions on bounded domains with tensor product splines. The main idea is to extend such functions and then use known approximation techniques on Rd. We prove an error estimate for domains for which bounded extension operators exist. This obvious approach has some limitations. It is not applicable without restrictions on the chosen coordinate degree even if the domain is as simple as the unit disk. Further for approximation on Rd there are error estimates in which the grid widths and directional derivatives are paired in an interesting way. It seems impossible to maintain this property using extension operators.
We introduce bloomRF as a unified method for approximate membership testing that supports both point- and range-queries. As a first core idea, bloomRF introduces novel prefix hashing to efficiently encode range information in the hash-code of the key itself. As a second key concept, bloomRF proposes novel piecewisemonotone hash-functions that preserve local order and support fast range-lookups with fewer memory accesses. bloomRF has near-optimal space complexity and constant query complexity. Although, bloomRF is designed for integer domains, it supports floating-points, and can serve as a multi-attribute filter. The evaluation in RocksDB and in a standalone library shows that it is more efficient and outperforms existing point-range-filters by up to 4× across a range of settings and distributions, while keeping the false-positive rate low.
