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arXiv · 1802.06545

Upper and lower bounds for dynamic data structures on strings

Raphael Clifford·Allan Grønlund·Kasper Green Larsen·Tatiana Starikovskaya
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Abstract

We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give both conditional and unconditional lower bounds for variants of exact matching with wildcards, inner product, and Hamming distance computation via a sequence of reductions. As an example, we show that there does not exist an $O(m^{1/2-\varepsilon})$ time algorithm for a large range of these problems unless the online Boolean matrix-vector multiplication conjecture is false. We also provide nearly matching upper bounds for most of the problems we consider.

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Raphael Clifford, Allan Grønlund, Kasper Green Larsen, Tatiana Starikovskaya. 2018-02-19. Upper and lower bounds for dynamic data structures on strings. https://arxiv.org/abs/1802.06545

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