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- W2750889557 abstract "We show that it is possible to store a dynamic ordered set S of n integers drawn from a bounded universe of size u in space close to the information-theoretic lower bound and preserve, at the same time, the asymptotic time optimality of the operations. Our results leverage on the Elias-Fano representation of monotone integer sequences, which can be shown to be less than half a bit per element away from the information-theoretic minimum.In particular, considering a RAM model with memory word size Theta(log u) bits, when integers are drawn from a polynomial universe of size u = n^gamma for any gamma = Theta(1), we add o(n) bits to the static Elias-Fano representation in order to:1. support static predecessor/successor queries in O(min{1+log(u/n), loglog n});2. make S grow in an append-only fashion by spending O(1) per inserted element;3. describe a dynamic data structure supporting random access in O(log n / loglog n) worst-case, insertions/deletions in O(log n / loglog n) amortized and predecessor/successor queries in O(min{1+log(u/n), loglog n}) worst-case time. These time bounds are optimal." @default.
- W2750889557 created "2017-09-15" @default.
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- W2750889557 date "2017-01-01" @default.
- W2750889557 modified "2023-09-23" @default.
- W2750889557 title "Dynamic Elias-Fano Representation." @default.
- W2750889557 doi "https://doi.org/10.4230/lipics.cpm.2017.30" @default.
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