Efficiently managing the history of a time-evolving system is one of the central problems in many database environments, like database systems that incorporate versioning, or object oriented databases that implicitly or explicitly maintain the history of persistent objects. In this proposal, we propose algorithms that reconstruct past states of an evolving system for two general cases, i.e., when the system's state is represented by a set or by a hierarchy (a forest of trees) and a hardware concept use this algorithm. Sets are widely used as a canonical form of representing information in databases or program states. For more complex applications, like schema evolution in object-oriented databases, it becomes necessary to manage the history of data structures that have the form of forests or even graphs. The proposed algorithms use minimal space (proportional to the number of changes occurring in the evolution) and have the advantage of on line (in the amortized sense). Any past system state s (t) is reconstructed in time 0(1 s(t)l + loglogT, where I s(t)l is the size of the answer and T is the maximal evolution time. For all practical cases the loglogT factor is a constant, therefore our algorithms provide almost random access to any past system state. The proposed algorithms are optimal among all algorithms that use space linear in the number of changes in the system's evolution. Anticipated Benefits/Potential Applications - -This approach to management of time-evolving databases applicable to many databases, both commercial and military. Weather business, global warming, and missile trajectory histories are examples of such databases.
