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- W2951802022 abstract "We introduce a new model for studying data structure problems -- the quantum cell probe We prove a lower bound for the predecessor problem in the address-only version of this model where we allow parallelism only over the `address lines' of the queries. The address-only cell probe model subsumes the classical cell probe model, and many query algorithms like Grover's algorithm fall into this framework. Our lower bound improves the previous known lower bound for the predecessor problem in the classical cell probe model with randomised query schemes, and matches the classical deterministic upper bound of Beame and Fich. Beame and Fich have also proved a matching lower bound for the predecessor problem, but only in the classical deterministic setting. Our lower bound has the advantage that it holds for the more general model, and also, its proof is substantially simpler than that of Beame and Fich. We prove our lower bound by obtaining a round elimination lemma for communication complexity. A similar lemma was proved by Miltersen, Nisan, Safra and Wigderson for classical communication complexity, but it was not strong enough to prove a lower bound matching the upper bound of Beame and Fich. Our round elimination lemma also allows us to prove rounds versus communication tradeoffs for some communication complexity problems like the greater-than problem. We also study the static membership problem in the cell probe model. Generalising a result of Yao, we show that if the storage scheme is implicit, that is it can only store members of the subset and `pointers', then any query scheme must make $Omega(log n)$ probes." @default.
- W2951802022 created "2019-06-27" @default.
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- W2951802022 date "2001-04-19" @default.
- W2951802022 modified "2023-09-27" @default.
- W2951802022 title "Lower bounds in the quantum cell probe model" @default.
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