Internal Masked Prefix Sums and Its Connection to Fully Internal Measurement Queries

Rathish Das, Meng He, Eitan Kondratovsky, J. Ian Munro, Kaiyu Wu

Abstract: We define a generalization of the prefix sum problem in which the vector can be masked by segments of a second (Boolean) vector. This problem is shown to be related to several other prefix sum, set intersection and approximate string match problems, via specific algorithms, reductions and conditional lower bounds. To our knowledge, we are the first to consider the fully internal measurement queries and prove lower bounds for them. We also discuss the hardness of the sparse variation in both static and dynamic settings. Finally, we provide a parallel algorithm to compute the answers to all possible queries when both vectors are fixed.