The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Fully dynamic point location in a monotone subdivision
SIAM Journal on Computing
Dynamic point location in general subdivisions
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Complexity models for incremental computation
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Lower bounds for union-split-find related problems on random access machines
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Randomized algorithms
On data structures and asymmetric communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Optimal Algorithms for List Indexing and Subset Rank
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Dynamic Algorithms for the Dyck Languages
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Sublogarithmic searching without multiplications
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Tight bounds for the partial-sums problem
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Information and Computation
Dynamic planar point location with sub-logarithmic local updates
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We give a number of new lower bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations.We study the signed prefix sum problem: given a string of length n of Os and signed ls, compute the sum of its ith prefix during updates. We show a lower bound of Ω(log n/log log n) time per operations, even if the prefix sums are bounded by log n/log log n during all updates. We also show that if the update time is bounded by the product of the worst-case update time and the answer to the query, then the update time must be Ω(√(log n/ log log n)).These results allow us to prove lower bounds for a variety of seemingly unrelated dynamic problems. We give a lower bound for the dynamic planar point location in monotone subdivisions of Ω(log n/ log log n) per operation. We give a lower bound for dynamic transitive closure on upward planar graphs with one source and one sink of Ω(log n/(log log n)2) per operation. We give a lower bound of Ω(√(log n/log logn)) for the dynamic membership problem of any Dyck language with two or more letters. This implies the same lower bound for the dynamic word problem for the free group with k generators. We also give lower bounds for certain range searching variants and for the dynamic prefix majority and prefix equality problems.