Abstract. We give new solutions to the SEARCHABLE PARTIAL SUMS WITH INDELS problem. Given a sequence of n k-bit numbers, we present a structure taking kn +o(kn) bits of space, able of performing operations sum, search, insert, and delete, all in O(log n) worst-case time, for any k = O(log n). This extends previous results by Hon et al. [2003c] achieving the same space and O(log n/ log log n) time complexities for the queries, yet offering complexities for insert and delete that are amortized and worse than ours, and supported only for k = O(1). Our result matches an existing lower bound for large values of k. We also give new solutions to the DYNAMIC SEQUENCE problem. Given a sequence of n symbols in the range [1, σ ] with binary zero-order entropy H 0 , we present a dynamic data structure that requires n H 0 + o(n log σ ) bits of space, which is able of performing rank and select, as well as inserting and deleting symbols at arbitrary positions, in O(log n log σ ) time. Our result is the first entropy-bound dynamic data structure for rank and select over general sequences. In the case σ = 2, where both previous problems coincide, we improve the dynamic solution of Hon et al. [2003c] in that we compress the sequence. The only previous result with entropy-bound space for dynamic binary sequences is by Blandford and Blelloch [2004] , which has the same complexities as our structure, but does not achieve constant 1 multiplying the entropy term in the space complexity. Finally, we present a new dynamic compressed full-text self-index, for a collection of texts over an alphabet of size σ , of overall length n and hth order empirical entropy H h .
A wavelet tree using dynamic bitmaps yields a dynamic sequence representation that takes nH 0 (T ) + o(n log σ) bits and solves all the operations in time O(log n log σ) REF .
Dynamic entropy-compressed sequences and full-text indexes
TALG
Mathematics Computer Science