Serializable graphs

Abstract

A database system is a collection of data items, read or written by transactions in a possibly interleaved fashion. An interleaved execution is assumed to be correct if the sequence of transaction steps, called history, is serializable, that is, the effect of the execution is equivalent to that of some serial execution of the transactions. We give a graph-theoretic analogue of serializable histories. We define a new class of graphs, called serializable graphs, whose properties are such that (i) a serializable graph can be associated with each serializable history, and this can be done for various notions of serializability of histories and for serializability under various sets of constraints, and (ii) a serializable history, in fact a serial one, can be associated with each serializable graph. We use serializable graphs to characterize in an intuitive manner serializable histories involving general multi-step transactions, where some data items may be accessed by several read and write steps in an arbitrary fashion, and those involving nested transactions. The main graph-theoretic properties used in these characterizations are a directed cutset matching property and graph contraction.