On the Redundancy of Succinct Data Structures

The redundancyof a succinct data structure is the difference between the space it uses and the appropriate information-theoretic lower bound. We consider the problem of representing binary sequences and strings succinctly using small redundancy. We improve the redundancy required to support the important operations of rank and select efficiently for binary sequences and for strings over small alphabets. We also show optimal density-sensitiveupper and lower bounds on the redundancy for systematicencodings of binary sequences.

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