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Abstract |
While operations rank and select on static bitvectors can be supported in constant time, lower bounds show that supporting updates raises the cost per operation to O(log n / log log n) on bitvectors holding n bits. This is a shame in scenarios where updates are possible but uncommon. We develop a representation of bitvectors that we call adaptive dynamic bitvector, which uses the asymptotically optimal n + o(n) bits of space and, if there are q queries per update, supports all the operations in O(log(n/q) / log log n) amortized time. Further, we prove that this time is worst-case optimal in the cell probe model. We describe a large number of applications of our representation to other compact dynamic data structures. |
