Historical queries along multiple lines of time evolution

Traditional approaches to addressing historical queries assume a single line of time evolution; that is, a system (database, relation) evolves over time through a sequence of transactions. Each transaction always applies to the unique, current state of the system, resulting in a new current state. There are, however, complex applications where the system's state evolves into multiple lines of evolution. In general, this creates a tree (hierarchy) of evolution lines, where each tree node represents the time evolution of a particular subsystem. Multiple lines create novel historical queries, such as vertical or horizontal historical queries. The key characteristic of these problems is that portions of the history are shared; answering historical queries should not necessitate duplication of shared histories as this could increase the storage requirements dramatically. Both the vertical and horizontal historical queries have two parts: a "search" part, where the time of interest is located together with the appropriate subsystem, and a reconstruction part, where the subsystem's state is reconstructed for that time. This article focuses on the search part; several reconstruction methods, designed for single evolution lines can be applied once the appropriate time of interest is located. For both the vertical and the horizontal historical queries, we present algorithms that work without duplicating shared histories. Combinations of the vertical and horizontal queries are possible, and enable searching in both dimensions of the tree of evolutions.