Upper and Lower Bounds for Dynamic Data Structures on Strings

Raphaël Clifford, Allan Grønlund, Kasper Green Larsen, Tatiana Starikovskaya, Marc Herbstritt
2018 Symposium on Theoretical Aspects of Computer Science  
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
more » ... range of these problems unless the online Boolean matrixvector multiplication conjecture is false. We also provide nearly matching upper bounds for most of the problems we consider.
doi:10.4230/lipics.stacs.2018.22 dblp:conf/stacs/CliffordGLS18 fatcat:p7fj4i7osbewnnu4yc5hqrcybq