Tight bounds for the partial-sums problem
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Lower bounds for dynamic connectivity
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Information and Computation
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
A little advice can be very helpful
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Dynamic range majority data structures
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We study the complexity of the dynamic partial sum problem in the cell-probe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer $\pm 1$ as an oracle and prove that the problem remains hard. This suggests which kind of information is hard to maintain. From these results, we derive a number of lower bounds for dynamic algorithms and data structures: We prove lower bounds for dynamic algorithms for existential range queries, reachability in directed graphs, planarity testing, planar point location, incremental parsing, and fundamental data structure problems like maintaining the majority of the prefixes of a string of bits. We prove a lower bound for reachability in grid graphs in terms of the graph's width. We characterize the complexity of maintaining the value of any symmetric function on the prefixes of a bit string.