Upper and Lower Bounds for Dynamic Data Structures on Strings

Raphael Clifford, Allan Grønlund, Green Kasper, Larsen, Tatiana Starikovskaya
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−ε) time algorithm for a large
more » ... gorithm 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. 2012 ACM Subject Classification Theory of computation → Pattern matching, Theory of computation → Cell probe models and lower bounds, Theory of computation → Sketching and sampling