Algorithms on Compressed Strings and Arrays

We survey the complexity issues related to several algorithmic problems for compressed one- and two-dimensional texts without explicit decompression: pattern-matching, equality-testing, computation of regularities, subsegment extraction, language membership, and solvability of word equations. Our basic problem is one- and two-dimensional pattern-matching together with its variations. For some types of compression the pattern-matching problems are unfeasible (NP-hard), for other types they are solvable in polynomial time and we discuss how to reduce the degree of corresponding polynomials.

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