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We consider the computational aspects of lossy data compression problem,where the compression error is determined by a cover of the data space. Wepropose an algorithm which reduces the number of partitions needed to find theentropy with respect to the compression error. In particular, we show that, inthe case of finite cover, the entropy is attained on some partition. We give analgorithmic construction of such partition.

Partition Reduction for Lossy Data Compression Problem