Optimal Bi-Weighted Binary Trees and the Complexity of Maintaining Partial Sums

@inproceedings{Hampapuram1993OptimalBB,
  title={Optimal Bi-Weighted Binary Trees and the Complexity of Maintaining Partial Sums},
  author={Haripriyan Hampapuram and Michael L. Fredman},
  booktitle={FOCS},
  year={1993}
}
Let A be an array. The partial sum problem concerns the design of a data structure for implementing the following operations. The operation update(j, x) has the effect A[j] ← A[j]+x , and the query operation sum(j) returns the partial sum ∑j i=1 A[i] . Our interest centers upon the optimal efficiency with which sequences of such operations can be performed, and we derive new upper and lower bounds in the semigroup model of computation. Our analysis relates the optimal complexity of the partial… CONTINUE READING