The complexity of Boolean functions
The complexity of Boolean functions
On the communication complexity of graph properties
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On the time-space complexity of reachability queries for preprocessed graphs
Information Processing Letters
New bounds in cell probe model
New bounds in cell probe model
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
On the cell probe complexity of polynomial evaluation
Theoretical Computer Science
On data structures and asymmetric communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Communication complexity
Lower bounds for high dimensional nearest neighbor search and related problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The Complexity of Some Simple Retrieval Problems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
The Bit Probe Complexity Measure Revisited
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A topological approach to evasiveness
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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We initiate a study of space-time tradeoffs in the cell-probe model under restricted preprocessing power. Classically, space-time tradeoffs have been studied in this model under the assumption that the preprocessing is unrestricted. In this setting, a large gap exists between the best known upper and lower bounds. Augmenting the model with a function family F that characterizes the preprocessing power, makes for a more realistic computational model and allows to obtain much tighter space-time tradeoffs for various natural settings of F. The extreme settings of our model reduce to the classical cell probe and generalized decision tree complexities. We use graph properties for the purpose of illustrating various aspects of our model across this broad spectrum. In doing so, we develop new lower bound techniques and strengthen some existing results. In particular, we obtain near-optimal space-time tradeoffs for various natural choices of F; strengthen the Rivest-Vuillemin proof of the famous AKR conjecture to show that no non-trivial monotone graph property can be expressed as a polynomial of sub-quadratic degree; and obtain new results on the generalized decision tree complexity w.r.t. various families F.