Making data structures confluently persistent

Amos Fiat, Haim Kaplan

Abstract: We address a longstanding open problem of [8, 7], and present a general transformation that takes any data structure and transforms it to a confluently persistent data structure. We model this general problem using the concepts of a version DAG (Directed Acyclic Graph) and an instantiation of a version DAG. We introduce the concept of the effective depth of a vertex in the version DAG and use it to derive information theoretic lower bounds on the space expansion of any such transformation for this DAG. We then give a confluently persistent data structure, such that for any version DAG, the time slowdown and space expansion match the information theoretic lower bounds to within a factor of Ο(log2(¦V¦)).