Bounded evaluation using views is to compute the answers $Q({\cal D})$ to a query $Q$ in a dataset ${\cal D}$ by accessing only cached views and a small fraction $D_Q$ of ${\cal D}$ such that the size $|D_Q|$ of $D_Q$ and the time to identify $D_Q$ are independent of $|{\cal D}|$, no matter how big ${\cal D}$ is. Though proven effective for relational data, it has yet been investigated for graph data. In light of this, we study the problem of bounded pattern matching using views. We first introduce access schema ${\cal C}$ for graphs and propose a notion of joint containment to characterize bounded pattern matching using views. We show that a pattern query $\sq$ can be boundedly evaluated using views ${\cal V}(G)$ and a fraction $G_Q$ of $G$ if and only if the query $\sq$ is jointly contained by ${\cal V}$ and ${\cal C}$. Based on the characterization, we develop an efficient algorithm as well as an optimization strategy to compute matches by using ${\cal V}(G)$ and $G_Q$. Using real-life and synthetic data, we experimentally verify the performance of these algorithms, and show that (a) our algorithm for joint containment determination is not only effective but also efficient; and (b) our matching algorithm significantly outperforms its counterpart, and the optimization technique can further improve performance by eliminating unnecessary input.
Some Properties of Algebra of Quotients with Bounded Evaluation of a Norm Ideal on Complex Banach Space
